The 5 kg block in the figure is pulled with a constant velocity of V . Initially springs are in natural length and 3kg block is at rest. (Take : ∣ V ∣ = 3 m/s , π 2 = 10 and K = 10 N/m) List-I List-II

Question

The 5 kg block in the figure is pulled with a constant velocity of $V$ . Initially springs are in natural length and 3kg block is at rest. (Take : $∣ V ∣ = 3 m/s, π^{2} = 10$ and K = 10 N/m)

List-I	List-II
(P) Time after which velocity of 3 kg block becomes $V$ (in sec)	(1) 40
(Q) Time after which 3 kg block comes to rest again (in sec)	(2) 2/3
(R) Displacement of 5 kg block when relative velocity between the blocks is zero (in m)	(3) 60
(S) External force required on 5 kg block when 3 kg block comes to rest again (in N)	(4) 2
	(5) 10

TestHub · Accepted Answer

In the frame moving with 2V/3, the 3 kg block executes SHM with $T = 2 π \frac{m}{3 k} = 2 π \frac{3}{30} = 2 sec$

(P) Block regains velocity V⃗ after $t = \frac{T}{3} = \frac{2}{3} s \to (2)$

(Q) Block comes to rest again after $t = T = 2 s \to (4)$

(R) Relative velocity zero at t = T/3: displacement of 5 kg block $= V t = 3 \times \frac{2}{3} = 2 m \to (4)$

(S) When 3 kg is at rest again, spring 2K is stretched by 2 m ⇒ external force $= 2 K \times 2 = 40 N \to (1)$

Hence (A).

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