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)

$\frac { 25 } { 24 }$

Answer 2

2 T sin 370⁰= 20

2 T × $\frac { 3 } { 5 }$ = 20

T = $\frac { 50 } { 3 }$ N

Now when spring in cut in case – 1 then net force F₁ acting on block is

F₁ = $\sqrt { ( 20 ) ^ { 2 } + \left( \frac { 50 } { 3 } \right) ^ { 2 } - 2 \times 20 \times \frac { 50 } { 3 } \times \frac { 3 } { 5 } }$ = $\frac { 50 } { 3 }$ N

and when string is cut in cse-2 then net force F₂ acting on block is F₂ = 20 × $\frac { 4 } { 5 }$ = 16 N

\ $\frac { a _ { 1 } } { a _ { 2 } }$ = $\frac { 50 } { 3 }$ × $\frac { 1 } { 16 }$ = $\frac { 50 } { 48 }$ = $\frac { 25 } { 24 }$