Units and Dimensions

Q.

One Angstrom is equal to how many meters?

Q. Write a short note on the triple point of water.

Q. The force is given in terms of time $t$ and displacement $x$ by the equation $F=A\cos Bx+C\sin Dt$. The dimensional formula of $\frac{AD}{B}$ is:

1. $\left[M^1{L}^1{T}^{-2}\right]$
2. $\left[M^2{L}^2{T}^{-3}\right]$
3. $\left[M{L}^2{T}^{-3}\right]$
4. $\left[M^{0}L{T}^{-1}\right]$

Q.

Find the value of 60Joule/min in a system100g, 100 cm, and 1 min as the base units.

Q. A particle is moving such that its position coordinates (x, y) are (2m, 3m) at time t = 0, (6m, 7m) at t = 2 sec and (13m, 14m) at time t = 5 sec. Average velocity vector $V_{avg}$ from t = 0 to t = 5 sec is:

1. $\frac{13\hat{i}+14\hat{j}}{4}$
2. $\left(\widehat{i+\hat{j}}\right)$
3. $\frac{7}{3}(\hat{i}+\hat{j})$
4. $\frac{11}{5}(\hat{i}+\hat{j})$

Q. If $x=at+b{t}^2$, where $x$ is the distance travelled by the body in kilometers while $t$ is the time in seconds, then the unit of $b$ is

1. $\text{Km/s}$
2. ${\text{Km/s}}^2$
3. $\text{Kms}$
4. ${\text{Kms}}^2$

Q.

The weighing machine measures weight of the body or mass of the body.

Q. The dimensional formula of modulus of rigidity is

1. $\text{M L T}{}^{-2}$
2. $\text{M L T}{}^{-1}$
3. $\text{M L}{}^2\text{T}{}^2$
4. $\text{M L}{}^{-1}\text{T}{}^{-2}$

Q. Which of the following pair has the same dimensions

1. Work and power
2. Density and relative density
3. Stress and strain
4. Momentum and impulse

Q. The dimensions of calorie are

1. $\text{M L}{}^2\text{T}{}^{-2}$
2. $\text{M L T}{}^{-2}$
3. $\text{M L}{}^2\text{T}{}^{-1}$
4. $\text{M L}{}^2\text{T}{}^{-3}$

Q. The metre is defined as the distance travelled by light in 1/299792458 second.why don't people choose some easier number such as 1/300000000 second?

Q. Expression for time in terms of $G$ (universal gravitational constant ), $h$ (Planck's constant) and $c$ (speed of light ) is proportional to

1. $\sqrt{\frac{Gh}{c^3}}$
2. $\sqrt{\frac{h{c}^5}{G}}$
3. $\sqrt{\frac{c^3}{Gh}}$
4. $\sqrt{\frac{Gh}{c^5}}$

Q. Which of the following pairs do not have identical dimensions ?

1. Pressure and stress
2. Work and pressure energy
3. Angular momentum and planck's constant
4. Moment of force and momentum

Q.

What is the meaning of derived quantities?

Q. $\text{[M L T}{}^{-1}\text{]}$ is dimensional formula of

1. Power
2. Momentum
3. Force
4. Couple

Q.

A physical quantity is measured and the result is
expressed as nu where u is the unit used and n is the
numerical value. If the result is expressed in various
units then .

Q. In a new system of units, the unit of mass is $100g$, unit of length is $4m$ and unit of time is $2s$. Find the numerical value of $10J$ in this system.

Q. Eight spherical drops of equal size are falling vertically through air with a terminal velocity $0.1{\text{ms}}^{-1}$. If the drops coalesce to form a large spherical drop, its terminal velocity would be

1. $0.1{\text{ms}}^{-1}$
2. $0.2{\text{ms}}^{-1}$
3. $0.3{\text{ms}}^{-1}$
4. $0.4{\text{ms}}^{-1}$

Q.

Calculate the ratio of kinetic energy of alpha particles and proton when they are placed in electric field E.

Q.

The SI unit of inductance, the henry can be written as

1. $\frac{weber}{Ampere}$

2. $\frac{Voltsecond}{Ampere}$

3. $\frac{Joule}{Amper{e}^2}$

4. All the above

Q.

What is dimension?

Q. Let $\left[{\in }_0\right]$ denote the dimensional formula of the permittivity of the vacuum and $\left[{\mu }_0\right]$ that of the permeability of the vacuum. If $M=$ mass, $L=$ length, $T=$ time and $I=$ electric current, then:
Given $F=\frac{1}{4\pi {\in }_0}.\frac{q_1{q}_2}{r^2}$, where $q_1$ and $q_2$ are charges and r is the distance. Also,
$c=\frac{1}{\sqrt{{\in }_0{\mu }_0}}$, where $c$ is speed.

1. $\left[{\in }_0\right]=\left[M^{-1}{L}^{-3}{T}^{2}I\right]$
2. $\left[{\in }_0\right]=\left[M^{-1}{L}^{-3}{T}^4{I}^2\right]$
3. $\left[{\mu }_0\right]=\left[ML{T}^{-2}{I}^{-2}\right]$
4. $\left[{\mu }_0\right]=\left[M{L}^2{T}^{-1}I\right]$

Q. A boy recalls the relation almost correctly but forgets where to put the constant $c$ i.e. speed of light. He writes $m=\frac{m_0}{\sqrt{1-v^2}}$, where $m$ and $m_0$ stand for masses and $v$ for speed. Right place of $c$ is

1. $m=\frac{c{m}_0}{\sqrt{1-v^2}}$
2. $m=\frac{m_0}{c\sqrt{1-v^2}}$
3. $m=\frac{m_0}{\sqrt{c^2-v^2}}$
4. $m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$

Q. The energy required to remove an electron in a hydrogen atom from n = 10 state is

1. 13.6 eV
2. 0.136 eV
3. 1.36 eV
4. 0.0136 eV

Q. A raindrop with radius $R=0.2\text{mm}$ falls from a cloud at a height $h=2000\text{m}$ above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is :
[Density of water ${\rho }_w=1000{\text{kg m}}^{-3}$ and density of air ${\rho }_a=1.2{\text{kg m}}^{-3},g=10{\text{m/s}}^2$
Coefficient of viscosity of air$=1.8\times {10}^{-5}{\text{Nsm}}^{-2}$

1. $250.6{\text{ms}}^{-1}$
2. $43.56{\text{ms}}^{-1}$
3. $4.94{\text{ms}}^{-1}$
4. $14.4{\text{ms}}^{-1}$

Q. The area of a square is $5.29{\text{cm}}^2.$ The area of $7$ such squares taking into account the significant figures is-

1. $37.03{\text{cm}}^2$
2. $37.0{\text{cm}}^2$
3. $37.030{\text{cm}}^2$
4. $37{\text{cm}}^2$

Q.

Give an example of dimensionless quantity but has a unit.

Q. If the velocity V, acceleration A and force F are taken as fundamental quantities instead of mass M, length L and time T, the dimensions of Young’s modulus Y would be

1. $F{A}^2{V}^{-4}$
2. $F{A}^2{V}^{-5}$
3. $F{A}^2{V}^{-3}$
4. $F{A}^2{V}^{-2}$

Q. With the usual notations, the following equation $S_n=u+\frac{1}{2}a(2n-1)$ is

1. only numerically correct.
2. only dimensionally correct.
3. both numerically and dimensionally correct.
4. neither numerically nor dimensionally correct.

Q. When a small sphere moves at low speed through a fluid, the viscous force $F$, opposing the motion is experimentally found to depend upon the radius $r$, the velocity $v$ of the sphere and the viscosity $\eta$ of the fluid. Expression of force is proportional to
Note: $\left[\eta \right]=\left[M{L}^{-1}{T}^{-1}\right]$

1. $\frac{\eta r}{v}$
2. $\eta rv$
3. ${\eta }^{2}rv$
4. ${\eta }^{2}r{v}^2$