Solved Example Problems
Convert 76 cm of mercury pressure into Nm−2 using the method of dimensions.
In cgs system 76 cm of mercury pressure = 76 × 13.6 × 980 dyne cm−2
The dimensional formula of pressure P is [ML−1T−2]
If the value of universal gravitational constant in SI is 6.6x10−11 Nm2 kg−2, then find its value in CGS System?
Let GSI be the gravitational constant in the SI system and Gcgs in the cgs system. Then
The dimensional formula for G is M−1 L3T −2
Check the correctness of the equation
using dimensional analysis method
Both sides are dimensionally the same, hence the equations
is dimensionally correct.
Obtain an expression for the time period T of a simple pendulum. The time period T depends on (i) mass ‘m’ of the bob (ii) length ‘l’ of the pendulum and (iii) acceleration due to gravity g at the place where the pendulum is suspended. (Constant k = 2π) i.e
Here k is the dimensionless constant. Rewriting the above equation with dimensions
Comparing the powers of M, L and T on both sides, a=0, b+c=0, -2c=1
Solving for a,b and c a = 0, b = 1/2, and c = −1/2
From the above equation T = k. m0 l1/2 g−1/2
The force F acting on a body moving in a circular path depends on mass of the body (m), velocity (v) and radius (r) of the circular path. Obtain the expression for the force by dimensional analysis method. (Take the value of k=1)
where k is a dimensionless constant of proportionality. Rewriting above equation in terms of dimensions and taking k = 1, we have
Comparing the powers of M, L and T on both sides
From the above equation we get