Chapter: Laws of Motion

A ball of mass \(\begin{align}0.15\,kg\end{align}\)is dropped from a height \(\begin{align}10\,m\end{align}\), strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is nearly \(\begin{align}(g=10\,m/{{s}^{2}})\end{align}\)

A truck is stationary and has a bob suspended by a light string, in a frame attached to the truck. The truck, suddenly moves to the right with an acceleration of \(\begin{align}a\end{align}\). The pendulum will tilt

A particle moving with velocity \(\begin{align}v\end{align}\) is acted by three forces shown by the vector triangle\(\begin{align}PQR\end{align}\). The velocity of the particle will

A rigid ball of mass \(\begin{align}m\end{align}\) strikes a rigid wall at \(\begin{align}60{}^\circ \end{align}\) and gets reflected without loss of speed as shown in the figure. The value of impulse imparted by the wall on the ball will be

A bullet of mass \(\begin{align}10\,g\end{align}\) moving horizontal with a velocity of \(\begin{align}400\,m/s\end{align}\) strikes a wood block of mass \(\begin{align}2\,kg\end{align}\) which is suspended by light inextensible string of length \(\begin{align}5\,m\end{align}\). As result, the centre of gravity of the block found to rise a vertical distance of \(\begin{align}10cm\end{align}\). The speed of the bullet after it emerges of horizontally from the block will be

The force \(\begin{align}F\end{align}\) acting on a particle of mass \(\begin{align}m\end{align}\) is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from \(\begin{align}0\end{align}\) to \(\begin{align}8\end{align}\)\(\begin{align}s\end{align}\)is

A balloon with mass \(\begin{align}m\end{align}\) is descending down with an acceleration \(\begin{align}a(where,\, a<g)\end{align}\). How much mass should be removed from it so that it starts moving up with an acceleration \(\begin{align}a\end{align}\) ?

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass \(\begin{align}1\text{ }kg\end{align}\)moves with a speed of \(\begin{align}12m{{s}^{{-1}}}\end{align}\)and the second part of mass \(\begin{align}2\text{ }kg\end{align}\)moves with \(\begin{align}8\,m{{s}^{{-1}}}\end{align}\)speed. If the third part flies off with \(\begin{align}4\,m{{s}^{{-1}}}\end{align}\)speed, then its mass is

Two spheres \(\begin{align}A\end{align}\) and \(\begin{align}B\end{align}\)of masses \(\begin{align}{{m}_{1}}\end{align}\) and \(\begin{align}{{m}_{2}}\end{align}\)respectively collide. \(\begin{align}A\end{align}\) is at rest initially and \(\begin{align}B\end{align}\)is moving with velocity \(\begin{align}v\end{align}\) along \(\begin{align}x-axis\end{align}\). After collision, \(\begin{align}B\end{align}\)has a velocity \(\begin{align}\frac{v}{2}\end{align}\) in a direction perpendicular to the original direction. The mass \(\begin{align}A\end{align}\) moves after collision in the direction

A man of \(\begin{align}50\,kg\end{align}\)mass is standing in a gravity free space at a height of \(\begin{align}10\,m\end{align}\) above the floor. He throws a stone of \(\begin{align}0.5\,kg\end{align}\)mass downwards with a speed \(\begin{align}2\,m{{s}^{{-1}}}\end{align}\). When the stone reaches the floor, the distance of the man above the floor will be

A body, under the action of a force \(\begin{align}F=6\overset{\wedge }{\mathop{i}}\,-8\overset{\wedge }{\mathop{j}}\,+10\overset{\wedge }{\mathop{k}}\,\end{align}\),acquires an acceleration of \(\begin{align}1\,m{{s}^{{-2}}}\end{align}\) . The mass of this body must be

A \(\begin{align}0.5\,kg\end{align}\)ball moving with a speed of \(\begin{align}12\,m/s\end{align}\)strikes a hard wall at an angle of \(\begin{align}30{}^\circ \end{align}\) with the wall. It is reflected with the same speed and at the same angle. If the ball is in contact with the wall for \(\begin{align}0.25\text{ }s\end{align}\), the average force acting on the wall is

A block of mass \(\begin{align}m\end{align}\) is placed on a smooth wedge of inclination\(\begin{align}\theta \end{align}\). The whole system is accelerated horizontally, so that the block does not slip on the wedge. The force exerted by the wedge on the block (\(\begin{align}g\end{align}\) is acceleration due to gravity) will be

An object of mass \(\begin{align}3\,kg\end{align}\) is at rest. If a force \(\begin{align}F=(6{{t}^{2}}\overset{\wedge }{\mathop{i}}\,+4t\overset{\wedge }{\mathop{j}}\,)\end{align}\)\(\begin{align}N\end{align}\) is applied on the object, then the velocity of the object at \(\begin{align}t=3s\end{align}\) is

A player takes \(\begin{align}0.1\,s\end{align}\)in catching a ball of mass \(\begin{align}150g\end{align}\) moving with velocity of \(\begin{align}20\,m/s\end{align}\). The force imparted by the ball on the hands of the player is

1 kg body explodes into three fragments. The ratio of their masses is \(\begin{align}1:1:3\end{align}\). The fragments of same mass move perpendicular to each other with speeds \(\begin{align}30\,m/s\end{align}\), while the heavier part remains in the initial direction. The speed of heavier part is

A particle of mass \(\begin{align}1\,kg\end{align}\) is thrown vertically upwards with speed \(\begin{align}100\,m/s\end{align}\). After \(\begin{align}5\,s\end{align}\), it explodes into two parts. One part of mass \(\begin{align}400g\end{align}\) comes back with speed \(\begin{align}25\,m/s\end{align}\), what is the speed of other part just after explosion?

A ball of mass \(\begin{align}3\,kg\end{align}\) moving with a speed of \(\begin{align}100\,m/s\end{align}\), strikes a wall at an angle \(\begin{align}60{}^\circ \end{align}\) (as shown in figure). The ball rebounds at the same speed and remains in contact with the wall for \(\begin{align}0.2\text{ }s\end{align}\), the force exerted by the ball on the wall is

The force on a rocket moving with a velocity \(\begin{align}300\text{ }m/s\end{align}\)is \(\begin{align}210\text{ }N\end{align}\). The rate of consumption of fuel of rocket is

A \(\begin{align}5000\text{ }kg\end{align}\)rocket is set for vertical firing. The exhaust speed is \(\begin{align}800\text{ }m{{s}^{{-1\text{ }}}}\end{align}\). To give an initial upward acceleration of \(\begin{align}20\text{ }m/{{s}^{2}}\end{align}\), the amount of gas ejected per second to supply the needed thrust will be \(\begin{align}\left( {g=10\text{ }m{{s}^{{-2}}}} \right)\end{align}\)

A bullet is fired from a gun. The force on the bullet is given by \(\begin{align}F=600-2\times {{10}^{5}}\text{ t}\end{align}\)where, \(\begin{align}\text{F}\end{align}\) is in newton and \(\begin{align}\text{t}\end{align}\) in second. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet?

A \(\begin{align}10\text{ }N\end{align}\)force is applied on a body produces an acceleration of \(\begin{align}1\text{ }m/{{s}^{2}}\end{align}\). The mass of the body is

A ball of mass \(\begin{align}150\text{ }g\end{align}\) moving with an acceleration \(\begin{align}20\text{ }m/{{s}^{2}}\end{align}\)is hit by a force, which acts on it for\(\begin{align}0.1\text{ }s\end{align}\). The impulsive force is

If the force on a rocket moving with a velocity of \(\begin{align}300\text{ }m/s\end{align}\) is \(\begin{align}345\text{ }N\end{align}\), then the rate of combustion of the fuel is

A satellite in a force free space sweeps stationary interplanetary dust at a rate. \(\begin{align}\left( {\frac{{dM}}{{dt}}} \right)=\alpha v\end{align}\). The acceleration of satellite is

Physical independence of force is a consequence of

A particle of mass \(\begin{align}m\end{align}\) is moving with a uniform velocity \(\begin{align}{{v}_{1}}\end{align}\) . It is given an impulse such that its velocity becomes \(\begin{align}{{v}_{2}}\end{align}\) . The impulse is equal to

A \(\begin{align}600\text{ }kg\end{align}\)rocket is set for a vertical firing. If the exhaust speed is \(\begin{align}1000\text{ }m{{s}^{{-1}}}\end{align}\) , the mass of the gas ejected per second to supply the thrust needed to overcome the weight of rocket is

Two bodies of mass \(\begin{align}4\text{ }kg\end{align}\) and \(\begin{align}6\text{ }kg\end{align}\) are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity \(\begin{align}g\end{align}\) is

A block of mass \(\begin{align}m\end{align}\) is placed on a smooth inclined wedge \(\begin{align}ABC\end{align}\) of inclination \(\begin{align}\theta \end{align}\) as shown in the figure. The wedge is given an acceleration a towards the right. The relation between \(\begin{align}a\end{align}\) and \(\begin{align}\theta \end{align}\) for the block to remain stationary on the wedge is

Two blocks \(\begin{align}A\end{align}\) and \(\begin{align}B\end{align}\) of masses \(\begin{align}3m\end{align}\) and \(\begin{align}m\end{align}\) respectively are connected by a massless and inextensible string. The whole system is suspended by a mass less spring as shown in figure. The magnitudes of acceleration of \(\begin{align}A\end{align}\) and \(\begin{align}B\end{align}\) immediately after the string is cut, are respectively

Three blocks \(\begin{align}A\text{ }B\end{align}\), and \(\begin{align}C\end{align}\) of masses\(\begin{align}4\text{ }kg\end{align}\), \(\begin{align}2\text{ }kg\end{align}\) and \(\begin{align}1\text{ }kg\end{align}\)respectively, are in contact on a frictionless surface, as shown. If a force of \(\begin{align}14\text{ }N\end{align}\) is applied on the \(\begin{align}4\text{ }kg\end{align}\)block, then the contact force between \(\begin{align}A\end{align}\) and \(\begin{align}B\end{align}\)is

A person of mass \(\begin{align}60\text{ }kg\end{align}\)is inside a lift of mass \(\begin{align}940\text{ }kg\end{align}\)and presses the button on control panel. The lift starts moving upwards with an acceleration \(\begin{align}1.0\text{ }m/{{s}^{2}}\end{align}\). If \(\begin{align}g\text{ }=10m/{{s}^{2}}\end{align}\) , the tension in the supporting cable is

The mass of a lift is \(\begin{align}2000\text{ }kg\end{align}\). When the tension in the supporting cable is \(\begin{align}28000\text{ }N\end{align}\), then its acceleration is

Three forces acting on a body are shown in the figure. To have the resultant force only along the \(\begin{align}y\end{align}\)-direction, the magnitude of the minimum additional force needed is

A monkey of mass \(\begin{align}20\text{ }kg\end{align}\)is holding a vertical rope. The rope will not break, when a mass of \(\begin{align}25\text{ }kg\end{align}\)is suspended from it but will break, if the mass exceeds \(\begin{align}25\text{ }kg\end{align}\). What is the maximum acceleration with which the monkey can climb up along the rope? \(\begin{align}\left( {Take\,g=10\text{ }m/{{s}^{2}}} \right)\end{align}\)

A man weighs \(\begin{align}80\text{ }kg\end{align}\). He stands on a weighing scale in a lift which is moving upwards with a uniform acceleration of \(\begin{align}5\text{ }m/{{s}^{2}}\end{align}\) . What would be the reading on the scale? \(\begin{align}\left( {Take\text{ }10\text{ }m/{{s}^{2}}} \right)\text{ }\end{align}\)

A lift of mass \(\begin{align}1000\text{ }kg\end{align}\) is moving upwards with an acceleration of \(\begin{align}1\text{ }m/{{s}^{2}}\end{align}\). The tension developed in the string, which is connected to lift is \(\begin{align}\left( {g=9.8\text{ }m/{{s}^{2}}} \right)\text{ }\end{align}\)

Two masses \(\begin{align}{{M}_{1}}=\text{ }5\text{ }kg,{{M}^{2}}=10kg\text{ }\end{align}\)are connected at the ends of an inextensible string passing over a frictionless pulley as shown. When masses are released, then acceleration of masses will be

A mass of \(\begin{align}1\text{ }kg\end{align}\) is suspended by a thread. It is \(\begin{align}1\end{align}\). lifted up with an acceleration \(\begin{align}4.9\text{ }m/{{s}^{2}}\end{align}\) , \(\begin{align}2\end{align}\). lowered with an acceleration \(\begin{align}4.9\text{ }m/{{s}^{2}}\end{align}\). The ratio of the tensions is

Calculate the acceleration of the block and trolly system shown in the figure. The coefficient of kinetic friction between the trolly and the surface is \(\begin{align}0.05.(g=10\text{ }m/{{s}^{2}}\end{align}\), mass of the string is negligible and no other friction exists).

Two particles \(\begin{align}A\end{align}\) and \(\begin{align}B\end{align}\) are moving in uniform circular motion in concentric circles of radii \(\begin{align}{{r}_{A}}\end{align}\) and \(\begin{align}{{r}_{B}}\end{align}\) with speed \(\begin{align}{{v}_{A}}\end{align}\) and \(\begin{align}{{v}_{B}}\end{align}\) respectively. Their time period of rotation is the same. The ratio of angular speed of \(\begin{align}A\end{align}\) to that of \(\begin{align}B\end{align}\) will be

A body of mass \(\begin{align}m\end{align}\) is kept on a rough horizontal surface \(\begin{align}\left( {coefficient\text{ }of\text{ }friction\text{ }=\text{ }\mu } \right)\end{align}\). Horizontal force is applied on the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given \(\begin{align}F\end{align}\), where \(\begin{align}F\end{align}\) is

Which one of the following statements is incorrect?

A block \(\begin{align}A\end{align}\) of mass \(\begin{align}{{m}_{1}}\end{align}\) rests on a horizontal table. \(\begin{align}A\end{align}\) light string connected to it passes over a frictionless pulley at the edge of table and from its other end another block \(\begin{align}B\end{align}\)of mass \(\begin{align}{{m}_{2}}\end{align}\) is suspended. The coefficient of kinetic friction between the block and the table is \(\begin{align}{{\mu }_{k}}\end{align}\) . When the block \(\begin{align}A\end{align}\) is sliding on the table, the tension in the string is

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches \(\begin{align}30{}^\circ \end{align}\), the box starts to slip and slides \(\begin{align}4.0\text{ }m\end{align}\) down the plank in \(\begin{align}4.0\text{ }s\end{align}\). The coefficients of static and kinetic friction between the box and the plank will be, respectively

A system consists of three masses \(\begin{align}{{m}_{1}},\text{ }{{m}_{2}}\end{align}\) and \(\begin{align}{{m}_{3}}\end{align}\) connected by a string passing over a pulley \(\begin{align}P\end{align}\). The mass \(\begin{align}{{m}_{1}}\end{align}\) hangs freely and \(\begin{align}{{m}_{2}}\end{align}\) and \(\begin{align}{{m}_{3}}\end{align}\) are on a rough horizontal table \(\begin{align}\left( {the\text{ }coefficient\text{ }of\text{ }friction\text{ }=\text{ }\mu } \right)\end{align}\). The pulley is frictionless and of negligible mass. The downward acceleration of mass \(\begin{align}{{m}_{1}}\end{align}\) is \(\begin{align}\left( {Assume,\text{ }{{\text{m}}_{1}}={{m}_{2}}={{m}_{3}}=m} \right)\end{align}\)

Three blocks with masses \(\begin{align}m,\,2m\end{align}\)and \(\begin{align}3m\end{align}\) are connected by strings, as shown in the figure. After an upward force \(\begin{align}F\end{align}\) is applied on block \(\begin{align}m\end{align}\), the masses move upward at constant speed \(\begin{align}v\end{align}\). What is the net force on the block of mass \(\begin{align}2m\end{align}\) ? (\(\begin{align}g\end{align}\) is the acceleration due to gravity).

The upper half of an inclined plane of inclination \(\begin{align}\theta \text{ }\end{align}\) is perfectly smooth while lower half is rough. \(\begin{align}A\end{align}\) block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by

A block of mass \(\begin{align}m\end{align}\) is in contact with the cart \(\begin{align}C\end{align}\) as shown in the figure. The coefficient of static friction between the block and the cart is \(\begin{align}\mu \end{align}\). The acceleration \(\begin{align}\alpha \end{align}\) of the cart that will prevent the block from falling satisfies

A block \(\begin{align}B\end{align}\)is pushed momentarily along a horizontal surface with an initial velocity \(\begin{align}v\end{align}\). If \(\begin{align}\mu \end{align}\) is the coefficient of sliding friction between \(\begin{align}B\end{align}\)and the surface, block \(\begin{align}B\end{align}\) will come to rest after a time IMAGE 16

The coefficient of static friction, \(\begin{align}{{\mu }_{s}}\end{align}\) , between block \(\begin{align}A\end{align}\) of mass \(\begin{align}2\,kg\end{align}\) and the table as shown in the figure, is \(\begin{align}0.2\end{align}\). What would be the maximum mass value of block \(\begin{align}B\end{align}\), so that the two blocks do not move ? The string and the pulley are assumed to be smooth and massless \(\begin{align}(g=10m/{{s}^{2}})\end{align}\)

A block of mass \(\begin{align}10\,kg\end{align}\)is placed on a rough horizontal surface having coefficient of friction\(\begin{align}\mu =0.5\end{align}\) . If a horizontal force of \(\begin{align}100\text{ }N\end{align}\) is applied on it, then the acceleration of the block will be \(\begin{align}(Takeg=10m/{{s}^{2}})\end{align}\)

A block has been placed on an inclined plane with the slope angle \(\begin{align}\theta \end{align}\), block slides down the plane at constant speed. The coefficient of kinetic friction is equal to

Consider, a car moving along a straight horizontal road with a speed of \(\begin{align}72\text{ }km/h\end{align}\). If the coefficient of static friction between the tyres and the road is \(\begin{align}0.5\end{align}\), the shortest distance in which the car can be stopped is \(\begin{align}(Take\,g=10m/{{s}^{2}})\end{align}\)

A heavy uniform chain lies on horizontal table top. If the coefficient of friction between the chain and the table surface is \(\begin{align}0.25\end{align}\), then the maximum friction of the length of the chain that can hang over one edge of the table is

Starting from rest, a body slides down a \(\begin{align}45{}^\circ \end{align}\) inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is

A block of mass \(\begin{align}10\,kg\end{align}\)is in contact against the inner wall of a hollow cylindrical drum of radius \(\begin{align}1\,m\end{align}\). The coefficient of friction between the block and the inner wall of the cylinder is \(\begin{align}0.1\end{align}\). The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be \(\begin{align}(g=10m/{{s}^{2}})\end{align}\)

One end of the string of length \(\begin{align}I\end{align}\) is connected to a particle of mass m and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed \(\begin{align}v\end{align}\), the net force on the particle (directed towards center) will be (\(\begin{align}T\end{align}\) represents the tension in the string)

A uniform circular disc of radius \(\begin{align}50\text{ }cm\end{align}\) at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of \(\begin{align}2.0\text{ }rad\,{{s}^{{-2}}}\end{align}\) . Its net acceleration in \(\begin{align}m{{s}^{{-2}}}\end{align}\) at the end of \(\begin{align}2.0\,s\end{align}\) is \(\begin{align}a\end{align}\) approximately

A car is negotiating a curved road of radius \(\begin{align}\text{R}\end{align}\). The road is banked at angle \(\begin{align}\theta \end{align}\). The coefficient of friction between the tyres of the car and the road is \(\begin{align}{{\mu }_{s}}\end{align}\) . The maximum safe velocity on this road is

A car of mass \(\begin{align}1000\text{ }kg\end{align}\) negotiates a banked curve of radius \(\begin{align}90\text{ }m\end{align}\) on a frictionless road. If the banking angle is \(\begin{align}45{}^\circ \end{align}\), the speed of the car is

A gramophone record is revolving with an angular velocity \(\begin{align}\omega \end{align}\). \(\begin{align}A\end{align}\) coin is placed at a distancer from the centre of the record. The static coefficient of friction is \(\begin{align}\mu \end{align}\). The coin will revolve with the record if

A ball of mass \(\begin{align}0.25\text{ }kg\end{align}\)attached to the end of a string of length \(\begin{align}1.96\text{ }m\end{align}\) is moving in a horizontal circle. The string will break if the tension is more than \(\begin{align}25\text{ }N\end{align}\). What is the maximum speed with which the ball can be moved ?

What will be the maximum speed of a car on a road turn of radius \(\begin{align}30\text{ }m\end{align}\), if the coefficient of friction between the tyres and the road is \(\begin{align}0.4\end{align}\) ? \(\begin{align}\left( {Takeg\text{ }=9.8\text{ }m/{{s}^{2}}} \right)\end{align}\)

Two racing cars of masses \(\begin{align}m\end{align}\) and \(\begin{align}4\,m\end{align}\) are moving in circles of radii \(\begin{align}r\end{align}\) and \(\begin{align}2\,r\end{align}\) respectively. If their speeds are such that each makes a complete circle in the same time, then the ratio of the angular speeds of the first to the second car is