Laws of motion NCERT Solutions Class 11 Physics - Solved Exercise Question 5.16

Question 5.16:
Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.
Solution:
The given system of two masses and a pulley can be represented as shown in the following figure:

Smaller mass, m1 = 8 kg
Larger mass, m2 = 12 kg
Tension in the string = T
Mass m2, owing to its weight, moves downward with acceleration a,and mass m1 moves upward.
Applying Newton’s second law of motion to the system of each mass:
For mass m1:
The equation of motion can be written as:
Tm1g = ma … (i)
For mass m2:
The equation of motion can be written as:
m2g T = m2a … (ii)
Adding equations (i) and (ii), we get:
(m2 - m1)g = (m1 + m2)a
∴ a = ( (m2 - m1) / (m1 + m2) )g    ....(iii)
= (12 - 8) / (12 + 8) X 10  =  4 X 10 / 20  =  2 ms-2
Therefore, the acceleration of the masses is 2 m/s2.
Substituting the value of a in equation (ii), we get:
m2 g - T = m2(m2 - m1)g / (m1 + m2)
T = (m2 - (m22 - m1m2) / (m1 + m2) )g
= 2m1m2g / (m1 + m2)
= 2 X 12 X 8 X 10 / (12 + 8)
= 96 N
Therefore, the tension in the string is 96 N.

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