In the arrangement shown in fig. `m_(1)=1kg, m_(2)=2 kg`. Pulleys are massless and strings are light. For what value of M, the mass `m_(1)` moves with constant velocity.

Options

A. `6kg`
B. `4kg`
C. `8kg`
D. `10kg`

Answer

C

Explanation

Mass `m_(1)` moves with constant velocity if tension in the lower string `T_(1) = m_(1) g = (1) (10) = 10N … (i)`
`:.` Tension in the upper string is
`T_(2) =2T_(1) =20N…(ii)`
Acceleration of block `M` is therefore
`a=(T_(2))/(M)=(20)/(M)...(iii)`
This is also the acceleration of pulley 2
Absolute acceleration of mass `m_(1)` is zero Thus acceleration of `m_(1)` relative to pulley 2 is upwards or acceleration of `m_(2)` with respect to pulley 2 is a downwards Drawing free body diagram of `m_(2)` with respect to pulley 2 Equation of motion gives
`20- (40)/(M) -10 =2a (40)/(M)` solving this we get `M =8kg`
.