Hello, here I am providing you the questions of physics of IIT JEE exam level as under:

Problem 1:-

Find the dimension of Force.

Solution:-

Force is numerically equal to the product of mass and acceleration

Force = mass x acceleration

or [F] = mass x velocity/time= mass x (displacement/(time)2) = mass x (length/(time)2)

= [M] x [LT-2] = [MLT-2]

Problem 2:-

Find the dimension of gravitational constant ’G’.

Solution:-

From Newton’s law of Gravitation, the exerted by one mass upon another is

F=G (m1 m2)/r2 or G=(Fr2)/(m1 m1 )

or [G] = [MLT-2][L2] / ([M][M]) = [M-1 L3 T-2 ]

We can find its SI unit which is m3/Kgs2.

Problem 3:-

Convert one Newton into dyne.

Solution:-

Dimensional formula for Newton = [MLT-2]

Or 1 N = 1 Kg m/s2 ; But 1 kg = 103 g and 1 m = 102 cm

Therefore 1 N = ((103 g)(102 cm))/s2 = 105 g cm/s2 = 105 dyne

Problem 4:-

Consider the formula, T=2π√(l/g)

Where T is the time period of oscillation of a simple pendulum in a simple harmonic motion, l and g are the length of the pendulum and gravitational constants respectively. Check this formula, whether it is correct or not, using the concept of dimension.

Solution:-
As we know [g] = [LT-2]

Therefore [T] = √(([L])/([LT-2])) = [T] s

Thus the above equation is dimensionally correct (homogenous) and later you will come to know that it is physically also correct.

Problem 5:-
Consider the formula s=ut -1/3 at2. Check this formula whether it is correct or not, using the concept of dimension.

Solution:-

Dimensionally

[L] = [LT-1] [T] – [LT-2] [T2]

=> [L] = [L] – [L]

In this case also the formula is dimensionally correct but, you know that it is physically incorrect as the correct formula is given by

S = ut + ½ at2

Question 1:-

If force, time and velocity are treated as fundamental quantities then dimensional formula of energy will be,

(a) [FTV] (b) [FT2V] (c) [FTV2] (d) [FT2V2]

Question 2:-

Which one of the following physical quantities do not have the same dimensions.

(a) Pressure, Young’s Modulus, Stress (b) Electromotive Force, Voltage, Potential

(c) Heat, Work, Energy (d) Electric Dipole, Electric Field, Flux

Question 3:-

The pairs having same dimensional formula-

(a) Angular Momentum, Torque

(b) Torque, Work

(c) Plank’s Constant, Boltzmann’s Constant

(d) Gas Constant, Pressure

Question 4:-

If F = ax + bt2 + c where F is force, x is distance and t is time. Then what is dimension of axc/bt2?

(a) [ML2T-2] (b) [MLT-2] (c) [M0L0T0] (d) [MLT-1]

Question 5:-

The dimensional formula for angular momentum is,

(a) [ML2T-2] (b) [ML2T-1] (c) [MLT-1] (d) [M0L2T-2]