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Acceleration versus x and potential energy versus x graph of a particle moving along X-axis are as shown
below. Mass of the particle is 1 kg and velocity at x = 0 is 4 $m s^{- 1}$ .
Match the following columns for x = 8m and mark the correct option from the codes given below
Column I
(A) Final kinetic energy
(B) Work done by conservative forces
(C) Total work done
(D) Work done by external forces
Column II
(p) 120J
(q) 240J
(r ) $-$ 120 J
(s) 128 J

.

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A B C D

p q r s

A B C D

p s r q

A B C D

s q p r

A B C D

s p r q

answer is B.

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Detailed Solution

$v_{f} - v_{i} = Area of a - x graph = 12 {ms}^{- 1}$

$∴ v_{f} = 12 + 4 = 16 {ms}^{- 1}$

$Δ KE = \frac{1}{2} m (v_{f}^{2} - v_{i}^{2}) = 12 OJ$

Total work done by all the forces $= Δ KE = 120 J$

Final KE, $K_{f} = \frac{1}{2} m v_{f}^{2} = 128 J$

Work done by conservative forces $= U_{i} - U_{f} = 240 J$

Work done by external forces = Total work done - Work done by conservative forces

$= - 120 J$

Hence, $A \to s, B \to q, C \to p, D \to r$

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