Question

two masses m1 and m2 are connected at the ends of a light inextensible string that passes over frictionless pulley.draw a free body diagram and hence find acceleration,tension in the string when the masses are released

Answer 1

see figure, here it is clearly shown free body diagram of given situation.

Let a is acceleration and T is tension in the string when the masses are released.

if we assume, m1 > m2

then, mass m1 will move downward and m2 will move upward.

so, m1g - T = m1a ......(1)

T - m2g = m2a ..........(2)

solving equations (1) and (2),

we get, (m1 - m2)g = (m1 + m2)a

⇒a = (m1 - m2)g/(m1 + m2)

hence, acceleration, a = (m1 - m2)g/(m1 + m2)

and tension, T = m2a + m2g [ from eq (2)]

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

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

= 2m1.m2g/(m1 + m2)