Question

31. Find the acceleration of mass and tension in the string when masses are released in the
given fig. where M1= 12 kg and M2=8 kg
M1​

Answer 1

Answer:

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 ,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:

T – m1g = 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) × 10  =  4 × 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:

m2g - T = m2(m2 - m1)g / (m1 + m2)

T = (m2 - (m22 - m1m2) / (m1 + m2) )g

=(2m1)(m2g) / (m1 + m2)

= 2 × 12 × 8 × 10 / (12 + 8)

= 96 N

Therefore, the tension in the string is 96 N.

I hope it helps.

Explanation: