31. A physical quantity that has a unit but no dimensions is:

(a) Plane angle

(b) Strain

(c) Gravitational Constant

(d) Reynold's Number

 

 

 

 

 

 

This objective question is based on NCERT Exemplar subjective Question.

32. What will be the length of the arc of a circle of radius 31.0 cm which subtends an angle of $\mathrm{\pi }/6$ at the centre?

(1) 16 mm

(2) 16.2 mm

(3) 16.2 cm

(4) 16.3 cm

This objective question is based on NCERT Exemplar subjective Question.

Calculate the solid angle subtended by the periphery of an area of \(1~\text{cm}^2\)${\mathrm{}}^{}$ at a point situated symmetrically at a distance of \(5~\text{cm}\) from the area:
1. \(3\times 10^{-2}~\text{steradian}\)
2. \(4\times 10^{-2}~\text{steradian}\)
3. \(4\times 10^{-1}~\text{steradian}\)
4. \(3\times 10^{-1}~\text{steradian}\)

34. The displacement of a progressive wave is represented by y = Asin ($\mathrm{\omega }$t —kx), where x is distance and t is time. The dimensional formula of $\mathrm{\omega }$ and k are, respectively;

$\left(1\right)<mspace\; width="1em"></mspace>\left[{\mathrm{LT}}^{-1}\right]<mspace\; width="1em"></mspace>\&<mspace\; width="1em"></mspace>\left[{\mathrm{T}}^{-1}\right]$
$\left(2\right)<mspace\; width="1em"></mspace>\left[{\mathrm{L}}^2{\mathrm{T}}^{-1}\right]<mspace\; width="1em"></mspace>\&<mspace\; width="1em"></mspace>\left[{\mathrm{LT}}^{-1}\right]$
$\left(3\right)<mspace\; width="1em"></mspace>\left[{\mathrm{T}}^{-1}\right]<mspace\; width="1em"></mspace>\&<mspace\; width="1em"></mspace>\left[{\mathrm{L}}^{-1}\right]$
$\left(4\right)<mspace\; width="1em"></mspace>\left[{\mathrm{LT}}^{-2}\right]<mspace\; width="1em"></mspace>\&<mspace\; width="1em"></mspace>\left[{\mathrm{T}}^{-2}\right]$

This objective question is based on NCERT Exemplar subjective Question.

35. Time for 20 oscillations of a pendulum is measured as ${\mathrm{t}}_1=39.6\mathrm{s}$; ${\mathrm{t}}_2=39.9\mathrm{s}$ and ${\mathrm{t}}_3=39.5\mathrm{s}$. What is the accuracy of the measurement?

$\left(1\right)<mspace\; width="1em"></mspace>\pm 0.2<mspace\; width="1em"></mspace>\sec$
$\left(2\right)<mspace\; width="1em"></mspace>\pm 0.02<mspace\; width="1em"></mspace>\sec$
$\left(3\right)<mspace\; width="1em"></mspace>\pm 2.0<mspace\; width="1em"></mspace>\sec$
$\left(4\right)<mspace\; width="1em"></mspace>\pm 0.3<mspace\; width="1em"></mspace>\sec$

This objective question is based on NCERT Exemplar subjective Question.

36. A new system of units is proposed in which the unit of mass is $\mathrm{\alpha }$ kg, unit of length $\mathrm{\beta }$ m and unit of time $\mathrm{\gamma }$ s. How much will 5 J measure in this new system?

(1) $\frac{\mathrm{\gamma }}{{\mathrm{\alpha }}^2\mathrm{\beta }}$

(2) $\frac{\mathrm{\gamma }}{\mathrm{\alpha \beta }}$

(3) $\frac{{\mathrm{\gamma }}^2}{{\mathrm{\alpha \beta }}^2}$

(4) $\frac{1}{{\mathrm{\alpha \beta }}^2}$

This objective question is based on NCERT Exemplar subjective Question.

37. The volume of a liquid flowing out per second of a pipe of length l and radius r is written by a student as $\mathrm{V}=\frac{\mathrm{\pi }}{8}\frac{{\mathrm{Pr}}^4}{\mathrm{\eta l}}$ where P is the pressure difference between the two ends of the pipe and $\mathrm{\eta }$ is the coefficient of the viscosity of the liquid having dimensional formula $\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-1}\right]$. Then,

(1) the equation is dimensionally correct.

(2) the equation is dimensionally incorrect.

(3) the equation may be or may not be dimensionally correct.

(4) Nothing can be said.

This objective question is based on NCERT Exemplar subjective Question.

38. A physical quantity X is related to four measurable quantities a, b, c, and d as follows $\mathrm{X}={\mathrm{a}}^2{\mathrm{b}}^3{\mathrm{c}}^{5/2}{\mathrm{d}}^{-2}$. The percentage error in measuring a, b, c, and d is 1%, 2%, 3%, and 4%, respectively. What is the percentage error in quantity X?

(1) 22.1 %

(2) 13.2 %

(3) 34.6 %

(4) 23.5 %

This objective question is based on NCERT Exemplar subjective Question.

39. In the expression $\mathrm{P}={\mathrm{EL}}^2{\mathrm{m}}^{-5}{\mathrm{G}}^{-2}$, E, m, L, and G denote energy, mass, angular momentum, and gravițational constant, respectively. Dimensions of P are:

$\left(1\right)<mspace\; width="1em"></mspace>\left[{\mathrm{M}}^1{\mathrm{L}}^2{\mathrm{T}}^{-1}\right]$
$\left(2\right)<mspace\; width="1em"></mspace>\left[{\mathrm{M}}^1{\mathrm{L}}^0{\mathrm{T}}^{-2}\right]$
$\left(3\right)<mspace\; width="1em"></mspace>\left[{\mathrm{M}}^0{\mathrm{L}}^0{\mathrm{T}}^0\right]$
$\left(4\right)<mspace\; width="1em"></mspace>\left[{\mathrm{M}}^2{\mathrm{L}}^0{\mathrm{T}}^1\right]$

This objective question is based on NCERT Exemplar subjective Question.

40. If the velocity of light c, Planck's constant h, and gravitational constant G are taken as fundamental quantities, then the dimensions of mass are:

$\left(1\right)<mspace\; width="1em"></mspace>\mathrm{m}=\mathrm{k}\sqrt{\frac{\mathrm{h}}{\mathrm{cG}}}$
$\left(2\right)<mspace\; width="1em"></mspace>\mathrm{m}=\mathrm{k}\sqrt{\frac{\mathrm{cG}}{\mathrm{h}}}$
$\left(3\right)<mspace\; width="1em"></mspace>\mathrm{m}=\mathrm{k}\sqrt{\frac{\mathrm{c}}{\mathrm{hG}}}$
$\left(4\right)<mspace\; width="1em"></mspace>\mathrm{m}=\mathrm{k}\sqrt{\frac{\mathrm{ch}}{\mathrm{G}}}$

This objective question is based on NCERT Exemplar subjective Question.