Question

In the arrangement shown in figure $m_1=1kg$ and $m_2=2kg$. Pulleys are massless and strings are light. For what value of $M$ the mass $m_1$ moves with constant velocity?(neglect friction)

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

Answer 1

The correct option is B $4kg$

Now, according to question, $m_1$ moves with

constant velocity

$\Rightarrow a^1-a=0\Rightarrow a^1=a$ ....(i)

From figure above ,

$T-m_{1}g=0\Rightarrow T=m_{1}g=1\times 9.8$

$\Rightarrow T=9.8N$ .....(ii)

$2T=Ma$

$\Rightarrow Ma=19.6$ (from (ii)) ...... (iii)

$m_{2}g-T=a+a^1=29$ (from (i))

$\Rightarrow 2a=2\times 9.8-9.8$

$\Rightarrow a=\frac{9.8}{2}=4.9m/s^2$

putting in (iii)

$M=\frac{19.6}{4.9}$

$\Rightarrow M=4kg$