Question

Find the acceleration of the block just after the horizontal string is burnt $(g=10{\text{ms}}^{-2},\sin {53}^{\circ }=\frac{4}{5},\cos {53}^{\circ }=\frac{3}{5})$

• A. $4{\text{ms}}^{-2}$
• B. $10{\text{ms}}^{-2}$
• C. $13.33{\text{ms}}^{-2}$
• D. $7.5{\text{ms}}^{-2}$

Answer 1

The correct option is C $13.33{\text{ms}}^{-2}$

Applying Newton's 2nd law, in the horizontal direction:

$T\sin {53}^{\circ }=ma...\left(1\right)$

and in the vertical direction,

$T\cos {53}^{\circ }-mg=0$

$\Rightarrow T\cos {53}^{\circ }=mg...\left(2\right)$

Using equations $\left(1\right)$ and $\left(2\right)$,

$\frac{T\sin {53}^{\circ }}{T\cos {53}^{\circ }}=\frac{a}{g}$

Given,

$g=10{\text{ms}}^{-2},\sin {53}^{\circ }=\frac{4}{5},\cos {53}^{\circ }=\frac{3}{5}$

$\Rightarrow \frac{4}{3}=\frac{a}{10}$

$\Rightarrow a=13.33{\text{ms}}^{-2}$

Hence, $\left(C\right)$ is the correct answer.