Equal amounts of work are performed on two bodies,A and B,initially at rest,and of masses M and 2M respectively.The relation between their speeds immediately after the work has been done on them is A)v_A = $\sqrt { 2 }$ v_B. B)v_A = 2v_B. C)v_A = v_B. D)v_B = $\sqrt { 2 }$ v_A. E)v_B = 2v_A.

Question

Quizplus · Accepted Answer

The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. Since equal work is done on both bodies, the kinetic energy imparted to each is the same. For body A, KE = 0.5 * M * vA^2, and for body B, KE = 0.5 * 2M * vB^2. Setting these equal gives M * vA^2 = 2M * vB^2, leading to vA = √2 * vB.

Equal Amounts of Work Are Performed on Two Bodies,A and B,initially