Question

As shown in the following figures, block of mass $2 \, kg$ is in equilibrium in the vertical plane.





At a certain instant right spring in case- $1$ and right string in case- $2$ are cut. Then the ratio of instantaneous acceleration of block in case- $1$ to case- $2$ just after the cutting is (strings and springs are ideal)

• A. $0$
• B. $1$
• C. $\frac{25}{24}$
• D. none of these

Answer 1

Answer: (C)

$2Tsin 37^\circ =20$
$2T\times \frac{3}{5}=20$
$T=\frac{50}{3}N$
Now when spring is cut in case- $1$ then net force $F_{1}$ acting on block is,
$F_{1}=\sqrt{\left(20\right)^{2} + \left(\frac{50}{3}\right)^{2} - 2 \times 20 \times \frac{50}{3} \times \frac{3}{5}}$ (resultant force of the remaining $T=\frac{50}{3}N$ and $mg=20N$ forces)
$=\frac{50}{3}N$
Similarly, when the string is cut in case- $2$ then net force $F_{2}$ acting on block is $F_{2}=20\times \frac{4}{5}=16 \, N$
$\therefore \frac{a_{1}}{a_{2}}=\frac{50}{3}\times \frac{1}{16}=\frac{50}{48}=\frac{25}{24}$