AB is a quarter of a smooth horizontal circular track of radius R . A particle P of mass m moves along the track from A to B under the action of following forces : List - I List - II (C) Work done by

Question

AB is a quarter of a smooth horizontal circular track of radius R . A particle P of mass m moves along the track from A to B under the action of following forces :

List - I	List - II
(C) Work done by $F_{3}$	(P) $2 FR$
(D) Work done by $F_{4}$	(Q) $\frac{1}{2} FR$
(A) Work done by $F_{1}$	(R) FR
(B) Work done by $F_{2}$	(S) $\frac{π FR}{2}$
	(T) $\frac{2 FR}{π}$

Column-I	Column-II
(A) Work done by F1 (always towards y-axis)	(P) $\sqrt{2}\,FR$
(B) Work done by F2 (always towards point B)	(Q) $\dfrac{1}{\sqrt{2}}FR$
(C) Work done by F3 (always along the tangent to path AB)	(R) $FR$
(D) Work done by F4 (always towards x-axis)	(S) $\dfrac{\pi FR}{2}$
	(T) $\dfrac{2FR}{\pi}$

TestHub · Accepted Answer

For (A) : Work done by F 1 ​ = FR For (B) : dW = F ⋅ d s = ( FRd θ ) cos θ = FR cos θ d θ W = ∫ 0 Π/4 ​ FR cos θ d θ = FR ( sin θ ) 0 Π/4 ​ = 2 ​ FR ​ For (C) : W = ∫ F ⋅ ds = F ( 2 π R ​ ) = 2 π FR ​ For (D) : W = ∫ F ⋅ d s = ( F ) ( R ) = FR

Physics - W.E.P. Question with Solution | TestHub

Options:

Doubts & Discussion