A block of mass10 kg is moving in x-direction with a constant speed of 10 m/s. It is subjected to a retarding force F=0.1xJ/m during its travel from x=20m to x=30cm. Its final kinetic energy will be : (A) 450J (B) 475J (C)250J (D) 275J

Answer: (B) 475 J

Initial K.E. = 1/2 mv2 = 1/2 (10) (10)2 = 500J

Retarding force, at x = 20m, F1 = 0.1 x 20 = 2N

Retarding force, at x = 30m, F2 = 0.1 x 30 = 3N

Average of retarding force, F = (2+3)/2 = 2.5 N

Work done by retarding force = Loss in K.E.

= F x s = 2.5 (30-20) = 25J

Final K.E. = Initial K.E. – loss in K.E.

= 500 – 25 = 475J

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