Question

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

In each case, $m_{1}=3\, kg$ and $m_{2}=4\, kg$. 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 $\left[g=10\, ms ^{-2}\right]$

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

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, $m_{1} =3\, kg$
$m_{2} =4\, kg$
$g =10\, m / s ^{2}$
$a_{1} =\frac{4 \times 10}{3+4}$
$=\frac{40}{7} m / s ^{2}$
For fig. (b)

$\left(m_{1}+m_{2}\right) a=\left(m_{2}-m_{1}\right) g$
$a =\left(\frac{m_{2}-m_{1}}{\left(m_{1}+m_{2}\right)}\right) y$
$=\left(\frac{4-3}{4+3}\right) \times 10$
$=\frac{10}{7} m / s ^{2}$