Chapter: Environmental Chemistry

The angle of 1′ (minute of arc) in radian is nearly equal to

The unit of thermal conductivity is :

The unit of permittivity of free space, \(\begin{align} {{\varepsilon }_{0}}\end{align}\)is

The value of Planck’s constant in SI unit is

In a particular system, the unit of length, mass and time are chosen to be 10 cm, 10 g and 0.1 s respectively. The unit of force in this system will be equivalent to

A screw gauge gives the following readings when used to measure the diameter of a wire
Main scale reading : 0 mm
Circular scale reading : 52 divisions
Given that, 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is

Time intervals measured by a clock give the following readings 1.25 s, 1.24 s, 1.27 s, 1.21 s and 1.28 s. What is the percentage relative error of the observations?

A screw gauge has least count of 0.01 mm and there are 50 divisions in its circular scale. The pitch of the screw gauge is

Taking into account of the significant figures, what is the value of 9.99 m − 0.0099 m?

The main scale of a vernier calliper has n divisions/cm. n divisions of the vernier scale coincide with \(\begin{align} (n-1)\end{align}\) divisions of main scale. The least count of the vernier callipers is

A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of −0.004 cm, the correct diameter of the ball is

In an experiment, four quantities \(\begin{align} a,b,c\end{align}\) and \(\begin{align} d\end{align}\) are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity \(\begin{align} P\end{align}\) is calculated \(\begin{align} P=\frac{{{{a}^{3}}{{b}^{2}}}}{{cd}}\%\end{align}\). Error in \(\begin{align} P\end{align}\) is

If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be

The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are 4% and 3% respectively, the maximum error in the measurement of density will be

The percentage errors in the measurement of mass and speed are 2% and 3% respectively. The error in kinetic energy obtained by measuring mass and speed, will be

In a vernier callipers N divisions of vernier scale coincide with N −1 divisions of main scale (in which length of one division is 1 mm). The least count of the instrument should be

A certain body weighs 22.42 g and has a measured volume of 4.7 cc. The possible error in the measurement of mass and volume are 0.01 g and 0.1 cc. Then, maximum error in the density will be

If force \( [F]\), acceleration \([a] \) and time \( [T]\) are chosen as the fundamental physical quantities. Find the dimensions of energy.

If \(\begin{align} E\end{align}\) and \(G\) respectively denote energy and gravitational constant. then \(\begin{align} \frac{E}{G}\end{align}\) has the dimensions of

Dimensions of stress are

A physical quantity of the dimensions of length that can be formed out of \(\begin{align} c\end{align}\), \(\begin{align} G\end{align}\) and \(\begin{align} \frac{{{{e}^{2}}}}{{4\pi {{\varepsilon }_{0}}}}\end{align}\)is [\(\begin{align} c\end{align}\) is velocity of light, \(\begin{align} G\end{align}\) is universal constant of gravitation and \(\begin{align} e\end{align}\)is charge]

If energy \(\begin{align} (E)\end{align}\), velocity \(\begin{align} (v)\end{align}\) and time \(\begin{align} (T)\end{align}\) are chosen as the fundamental quantities, the dimensional formula of surface tension will be

If dimensions of critical velocity \(\begin{align} {{V}_{c}}\end{align}\) of a liquid flowing through a tube are expressed as \(\begin{align} \left[ {{{\eta }^{x}}{{\rho }^{y}}{{r}^{z}}} \right]\end{align}\), where \(\begin{align} \eta ,\rho \end{align}\) and \(\begin{align} r\end{align}\) are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of \(\begin{align} x,y\end{align}\)and \(\begin{align} z\end{align}\)are given by

If force \(\begin{align} (F)\end{align}\), velocity \(\begin{align} (v)\end{align}\)and time \(\begin{align} (T)\end{align}\) are taken as fundamental units, then the dimensions of mass are

The dimensions of \(\begin{align} {{({{\mu }_{0}}{{\varepsilon }_{0}})}^{{{{-1}}/{2}\;}}}\end{align}\)are

The dimensions of \(\begin{align} \frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}\end{align}\), where \(\begin{align} {{\varepsilon }_{0}}\end{align}\) is permittivity of free space and \(\begin{align} E\end{align}\) is electric field, are

If the dimensions of a physical quantity are given by\(\begin{align} \left[ {{{M}^{a}}{{L}^{b}}{{T}^{c}}} \right]\end{align}\), then the physical quantity will be

Which two of the following five physical parameters have the same dimensions?
(i) Energy density
(ii)Refractive index
(iii)Dielectric constant
(iv)Young’s modulus
(v)Magnetic field

Dimensions of resistance in an electrical circuit, in terms of dimension of mass\(\begin{align} M\end{align}\),of length\(\begin{align} L\end{align}\),of time\(\begin{align} T\end{align}\)and of current \(\begin{align} I\end{align}\),would be

The velocity v of a particle at time \(\begin{align} t\end{align}\) is given by \(\begin{align} v=at+\frac{b}{{t+c}}\end{align}\),where \(\begin{align} a,b\end{align}\) and \(\begin{align} c\end{align}\) are constants. The dimensions of \(\begin{align} a,b\end{align}\) and \(\begin{align} c\end{align}\)are respectively

The ratio of the dimensions of Planck’s constant and that of the moment of inertia is the dimension of

The dimensions of universal gravitational constant are

Planck’s constant has the dimensions of

A pair of physical quantities having same dimensional formula is

The dimensional formula for magnetic flux is

The force \(\begin{align} F\end{align}\)on a sphere of radius \(\begin{align} r\end{align}\) moving in a medium with velocity \(\begin{align} v\end{align}\) is given by \(\begin{align} F=6\pi \eta rv\end{align}\). The dimensions of \(\begin{align} \eta \end{align}\) are

Which of the following will have the dimensions of time ?

An equation is given as \(\begin{align} \left( {p+\frac{a}{{{{V}^{2}}}}} \right)=b\frac{\theta }{V}\end{align}\), where \(\begin{align} p=\end{align}\) pressure, \(\begin{align} V=\end{align}\)volume and \(\begin{align} \theta =\end{align}\) absolute temperature. If \(\begin{align} a\end{align}\) and \(\begin{align} b\end{align}\)are constants, then dimensions of \(\begin{align} a\end{align}\) will be

Which of the following is a dimensional constant ?

Turpentine oil is flowing through a tube of length \(\begin{align} l\end{align}\) and radius \(\begin{align} r\end{align}\). The pressure difference between the two ends of the tube is \(\begin{align} p\end{align}\). The viscosity of oil is given by \(\begin{align} \eta =\frac{{p({{r}^{2}}-{{x}^{2}})}}{{4vl}}\end{align}\) where, \(\begin{align} v\end{align}\) is the velocity of oil at distance \(\begin{align} x\end{align}\) from the axis of the tube. The dimensions of \(\begin{align} \eta \end{align}\) are

The time dependence of physical quantity \(\begin{align} p\end{align}\) is given by \(\begin{align} p-{{p}_{0}}\end{align}\) exp \(\begin{align} (-\alpha {{t}^{2}})\end{align}\), where \(\begin{align} \alpha \end{align}\) is a constant and \(\begin{align} t\end{align}\) is the time. The constant α

If p represents radiation pressure, \(\begin{align} c\end{align}\) represents speed of light and \(\begin{align} S\end{align}\) represents radiation energy striking unit area per sec. The non-zero integers \(\begin{align} x,y,z\end{align}\), such that \(\begin{align} {{p}^{x}}{{S}^{y}}{{c}^{z}}\end{align}\) is dimensionless are

The dimensional formula for permeability of free space, \(\begin{align} {{\mu }_{0}}\end{align}\) is

The frequency of vibration \(\begin{align} f\end{align}\)of a mass \(\begin{align} m\end{align}\) suspended from a spring of spring constant \(\begin{align} k\end{align}\) is given by a relation of the type \(\begin{align} f=C{{m}^{x}}{{k}^{y}}\end{align}\), where \(\begin{align} C\end{align}\) is a dimensionless constant. The values of \(\begin{align} x\end{align}\) and \(\begin{align} y\end{align}\) are

According to Newton, the viscous force acting between liquid layers of area \(\begin{align} A\end{align}\)and velocity gradient \(\begin{align} \frac{{\Delta v}}{{\Delta z}}\end{align}\) is given \(\begin{align} F=-\eta A\frac{{dv}}{{dz}}\end{align}\),where \(\begin{align} \eta \end{align}\) is constant called

The dimensional formula of pressure is

The dimensional formula of torque is

If \(\begin{align} x=at+b{{t}^{2}}\end{align}\) ,where \(\begin{align} x\end{align}\) is the distance travelled by the body in kilometer while \(\begin{align} t\end{align}\) is the time in second, then the unit of \(\begin{align} b\end{align}\) is

Dimensional formula of self-inductance is

Of the following quantities, which one has dimensions different from the remaining three?

The dimensional formula for angular momentum is

If \(\begin{align} C\end{align}\) and \(\begin{align} R\end{align}\)denote capacitance and resistance respectively, then the dimensional formula of \(\begin{align} CR\end{align}\) is