Question

Two bodies of equal masses are connected by a light inextensible string passing over a smooth frictionless pulley. The percent of mass that should be transferred from one to another, so that both the masses move $50\text{m}$ in $5\text{s}$ is

• A. $30\%$
• B. $40\%$
• C. $70\%$
• D. $50\%$

Answer 1

The correct option is B $40\%$

Both the masses will more with equal magnitude of acceleration in opposite direction.


Applying $3^{\text{rd}}$ equation of motion:

$S=ut+\frac{1}{2}a{t}^2$

$(\because u=0;S=50\text{m};t=5\text{sec})$

$\Rightarrow 50=\frac{1}{2}\times a\times 25$

$\therefore a=\frac{100}{25}=4{\text{m/s}}^2$

Let $m_1>m_2$, thus net pulling force on system of $m_1$ and $m_2$ is $(m_{1}g-m_{2}g)$.

$\Rightarrow a=\frac{F_{net}}{m_{system}}=\frac{(m_1-m_2)g}{m_1+m_2}$

$\Rightarrow 4=\frac{m_1-m_2}{m_1+m_2}\times 10$

Thus, $\frac{m_1-m_2}{m_1+m_2}=\frac{4}{10}=\frac{2}{5}$

Therefore, $\%$ of mass transferred from $m_2$ to $m_1$ will be given by,

% mass transferred $=\frac{(m_1-m_2)}{m_1+m_2}\times 100=\frac{2}{5}\times 100=40\%$

Hence correct option is $\left(b\right)$.