Question

As shown in the following figures, block of mass $2kg$ 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)

$2Tsin37^{\circ }=20$
$2T\times \frac{3}{5}=20$
$T=\frac{50}{3}N$
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 $F_2=20\times \frac{4}{5}=16N$
$\therefore \frac{a_1}{a_2}=\frac{50}{3}\times \frac{1}{16}=\frac{50}{48}=\frac{25}{24}$