Four balls P, Q, R and S move on a smooth horizontal track

PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

Four balls P, Q, R and S move on a smooth horizontal track. • The masses are related as: mQ=2mPm_Q = 2m_P, mR=3mPm_R = 3m_P, mS=mPm_S = m_P. • Their speeds are related as: vP=vv_P = v, vQ=vv_Q = v, vR=v2v_R = \dfrac{v}{2}, vS=2vv_S = 2v. Answer the following on the basis of this information. (i) Arrange the four balls in decreasing order of their kinetic energy. (ii) Identify the pair of balls that have equal kinetic energy, if any, and justify your answer. (iii) A student claims that doubling the mass always produces a larger increase in kinetic energy than doubling the speed. Evaluate this claim using the data for balls P and S and state whether it is valid or not. (iv) If the speed of ball R is suddenly doubled while its mass remains unchanged, explain qualitatively how its position in the order obtained in part (i) will change.

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