# Units and Dimensions

## Trending Questions

**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=AcosBx+CsinDt. The dimensional formula of ADB is:

- [M1L1T−2]
- [M2L2T−3]
- [ML2T−3]
- [M0LT−1]

**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 Vavg from t = 0 to t = 5 sec is:

- 13^i+14^j4
- (^i+^j)
- 73(^i+^j)
- 115(^i+^j)

**Q.**If x=at+bt2, where x is the distance travelled by the body in kilometers while t is the time in seconds, then the unit of b is

- Km/s
- Km/s2
- Kms
- Kms2

**Q.**

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

**Q.**The dimensional formula of modulus of rigidity is

- M L T−2
- M L T−1
- M L2 T2
- M L−1 T−2

**Q.**Which of the following pair has the same dimensions

- Work and power
- Density and relative density
- Stress and strain
- Momentum and impulse

**Q.**The dimensions of calorie are

- M L2 T−2
- M L T−2
- M L2 T−1
- M L2 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

- √Ghc3
- √hc5G
- √c3Gh
- √Ghc5

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

- Pressure and stress
- Work and pressure energy
- Angular momentum and planck's constant
- Moment of force and momentum

**Q.**

What is the meaning of derived quantities?

**Q.**[M L T−1] is dimensional formula of

- Power
- Momentum
- Force
- 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 100 g, unit of length is 4 m and unit of time is 2 s. Find the numerical value of 10 J in this system.

**Q.**Eight spherical drops of equal size are falling vertically through air with a terminal velocity 0.1 ms−1. If the drops coalesce to form a large spherical drop, its terminal velocity would be

- 0.1 ms−1
- 0.2 ms−1
- 0.3 ms−1
- 0.4 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

$\frac{weber}{Ampere}$

$\frac{Voltsecond}{Ampere}$

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

All the above

**Q.**

What is dimension?

**Q.**Let [∈0] denote the dimensional formula of the permittivity of the vacuum and [μ0] that of the permeability of the vacuum. If M= mass, L= length, T= time and I= electric current, then:

Given F=14π∈0.q1q2r2, where q1 and q2 are charges and r is the distance. Also,

c=1√∈0μ0, where c is speed.

- [∈0]=[M−1L−3T2I]
- [∈0]=[M−1L−3T4I2]
- [μ0]=[MLT−2I−2]
- [μ0]=[ML2T−1I]

**Q.**A boy recalls the relation almost correctly but forgets where to put the constant c i.e. speed of light. He writes m=m0√1−v2, where m and m0 stand for masses and v for speed. Right place of c is

- m=cm0√1−v2
- m=m0c√1−v2
- m=m0√c2−v2
- m=m0√1−v2c2

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

- 13.6 eV
- 0.136 eV
- 1.36 eV
- 0.0136 eV

**Q.**A raindrop with radius R=0.2 mm falls from a cloud at a height h=2000 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 ρw=1000 kg m−3 and density of air ρa=1.2 kg m−3, g=10 m/s2

Coefficient of viscosity of air=1.8×10−5 Nsm−2

- 250.6 ms−1
- 43.56 ms−1
- 4.94 ms−1
- 14.4 ms−1

**Q.**The area of a square is 5.29 cm2. The area of 7 such squares taking into account the significant figures is-

- 37.03 cm2
- 37.0 cm2
- 37.030 cm2
- 37 cm2

**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

- FA2V−4
- FA2V−5
- FA2V−3
- FA2V−2

**Q.**With the usual notations, the following equation Sn=u+12a(2n−1) is

- only numerically correct.
- only dimensionally correct.
- neither numerically nor dimensionally correct.
- both numerically and 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 η of the fluid. Expression of force is proportional to

Note: [η]=[ML−1T−1]

- ηrv
- ηrv
- η2rv
- η2rv2