In each case, $m_1=3 \mathrm{~kg}$ and $m_2=4 \mathrm{~kg}$. 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 [ $g=10 \mathrm{~ms}^{-2}$ ]
Two situations are shown in fig. (a) and (b). In each case, $m_1=3 \mathrm{~kg}$ and $m_2=4 \mathrm{~kg}$.…
In each case, $m_1=3 \mathrm{~kg}$ and $m_2=4 \mathrm{~kg}$. 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 [ $g=10 \mathrm{~ms}^{-2}$ ]
- $\frac{20}{7} \mathrm{~ms}^{-2}, \frac{10}{7} \mathrm{~ms}^{-2}$
- $\frac{10}{7} \mathrm{~ms}^{-2}, \frac{25}{7} \mathrm{~ms}^{-2}$
- $\frac{40}{7} \mathrm{~ms}^{-2}, \frac{10}{7} \mathrm{~ms}^{-2}$
- $\frac{30}{7} \mathrm{~ms}^{-2}, \frac{5}{7} \mathrm{~ms}^{-2}$
Solution
From $(i) \&(i i)$, we get $ a_1=\frac{m_2 g}{m_1+m_2} $ as $m_1=3 \mathrm{~kg}, m_2=4 \mathrm{~kg}$ $ a_1=\frac{4 \times 10}{3+4}=\frac{40}{7} \mathrm{~m} / \mathrm{s}^2 $ For fig. (b) $ a=\left(\frac{m_2-m_1}{\left(m_1+m_2\right)}\right) g=\frac{10}{7} \mathrm{~m} / \mathrm{s}^2 $
Asked in: AP EAMCET 2017 (26 Apr Shift 1)