A plank P is placed on a solid cylinder S, which rolls on a horizontal

1.	A plank P is placed on a solid cylinder S, which rolls on a horizontal surface. The two are of equal mass. There is no slipping at any of the surfaces in contact. The ratio of the kinetic energy of P to that of S is (a) 1 : 1 (b) 2 : 1 (c) 8 : 3 (d) 11 : 8
Answer» Correct Answer is: (c) 8 : 3 Let v be the velocity of the centre of mass of the cylinder S. Then, the velocity of P is 2v. ∴ KE of P is 1/2 (m)(2v)² = 2mv². KE of S is 1/2 mv²(1 + k²/r²) = 1/2 mv²(1 + 1/2) = 3/4 mv². ∴ The ratio becomes 2mv² : 3/4 mv² = 8 : 3.

A plank P is placed on a solid cylinder S, which rolls on a horizontal surface. The two are of equal mass. There is no slipping at any of the surfaces in contact. The ratio of the kinetic energy of P to that of S is (a) 1 : 1 (b) 2 : 1 (c) 8 : 3 (d) 11 : 8

Answer»

Correct Answer is: (c) 8 : 3

Let v be the velocity of the centre of mass of the cylinder S. Then, the velocity of P is 2v.

∴ KE of P is 1/2 (m)(2v)² = 2mv².

KE of S is 1/2 mv²(1 + k²/r²) = 1/2 mv²(1 + 1/2) = 3/4 mv².

∴ The ratio becomes

2mv² : 3/4 mv² = 8 : 3.

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A plank P is placed on a solid cylinder S, which rolls on a horizontal surface. The two are of equal mass. There is no slipping at any of the surfaces in contact. The ratio of the kinetic energy of P to that of S is (a) 1 : 1 (b) 2 : 1 (c) 8 : 3 (d) 11 : 8

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