Question

Two situations are shown in fig. (a) and (b).

In each case, $m_1=3kg$ and $m_2=4kg$. If $a_1,a_2$ are the respective accelerations of the blocks in these situations, then the values of $a_1$ and $a_2$ are respectively $\left[g=10m{s}^{-2}\right]$

• A. $\frac{20}{7}m{s}^{-2},\frac{10}{7}m{s}^{-2}$
• B. $\frac{10}{7}m{s}^{-2},\frac{25}{7}m{s}^{-2}$
• C. $\frac{40}{7}m{s}^{-2},\frac{10}{7}m{s}^{-2}$
• D. $\frac{30}{7}m{s}^{-2},\frac{5}{7}m{s}^{-2}$

Answer 1

Answer: (C)

For fig. (a)

$\left(m_1+m_2\right)a_1=m_{2}g$
$a_1=\frac{m_{2}g}{m_1+m_2}$
Given, $m_1=3kg$
$m_2=4kg$
$g=10m/s^2$
$a_1=\frac{4\times 10}{3+4}$
$=\frac{40}{7}m/s^2$
For fig. (b)

$\left(m_1+m_2\right)a=\left(m_2-m_1\right)g$
$a=\left(\frac{m_2-m_1}{\left(m_1+m_2\right)}\right)y$
$=\left(\frac{4-3}{4+3}\right)\times 10$
$=\frac{10}{7}m/s^2$