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

Options

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

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 diagrams of `m_(2)` with respect to pulley 2 Equation of motion gives
`20-40/M-10=2a=40/M`
Solving this we get `M=8` kg