A block A of mass m is moving on a frictionless horizontal plane towards a smooth wedge (B) of mass 2 m , which is kept at rest on smooth horizontal plane at t = 0 , At t = t 1 , it is found that bo

Question

A block A of mass m is moving on a frictionless horizontal plane towards a smooth wedge (B) of mass 2 m , which is kept at rest on smooth horizontal plane at t = 0 , At t = t 1 ​ , it is found that both block & wedge is moving with same velocity and at t = t 2 ​ it is found that block & wedge are again moving on the horizontal frictionless plane. In list-I work done by different forces are given and in list-II value of work done by those forces are given. Column I Column II (P) Work done by gravity on block A from t = 0 to t = t 1 ​ (1) − 9 m v 2 ​ (Q) Work done by normal force exerted by wedge on the block A from t = 0 to t = t 1 ​ (2) 3 m v 2 ​ (R) Work done by the normal force exerted by block A on the wedge for t = t 1 ​ to t = t 2 ​ (3) Zero (S) Work done by the gravity on block A from t = 0 to t = t 2 ​ . (4) − 3 m v 2 ​ (5) 2 m v 2 ​

TestHub · Accepted Answer

W g ​ = − Δ K W g ​ = − 2 1 ​ m ( v 3 ​ ) 2 = − m v 3 2 ​ ⇒ P → ( 4 ) (Q) Normal force of wedge on block A ( 0 → t 1 ​ ) W N ​ = − m v 3 2 ​ ⇒ Q → ( 1 ) (R) Normal force of block A on wedge ( t 1 ​ → t 2 ​ ) W = Δ K = 2 1 ​ m ( v 3 ​ ) 2 = m v 3 2 ​ ⇒ R → ( 2 ) (S) Gravity on block A ( 0 → t 2 ​ ) W g ​ = m g ( h 2 ​ − h 0 ​ ) = 0 ⇒ S → ( 3 ) P → 4 , Q → 1 , R → 2 , S → 3

Column I	Column II
(P) Work done by gravity on block A from $t = 0$ to $t = t_{1}$	(1) $- \frac{m v ^{2}}{9}$
(Q) Work done by normal force exerted by wedge on the block A from $t = 0$ to $t = t_{1}$	(2) $\frac{m v ^{2}}{3}$
(R) Work done by the normal force exerted by block A on the wedge for $t = t_{1}$ to $t = t_{2}$	(3) Zero
(S) Work done by the gravity on block A from $t = 0$ to $t = t_{2}$ .	(4) $- \frac{m v ^{2}}{3}$
	(5) $\frac{m v ^{2}}{2}$

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JEE Advanced 2028 (Class 11)