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Physics-

General

Easy

Question

A hollow sphere is released from the top of a wedge, friction is sufficient for pure rolling of sphere on the wedge. There is no friction between the wedge and the ground. Radius of sphere is R. At the instant it leaves the wedge horizontally. Velocity of centre of mass of sphere w.r.t. ground is-

$\sqrt{\frac{5}{7} g h}$
$\sqrt{2 g h}$
$\sqrt{\frac{3}{7} g h}$
$\sqrt{\frac{11}{7} g h}$

The correct answer is: $square root of fraction numerator 3 over denominator 7 end fraction g h end root$

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A mouse, searching for food, jumped onto the rim of a stationary circular disk mounted on a vertical axle. The disk is free to rotate without friction. The velocity of the mouse was tangent to the edge of the disk before it landed. When the mouse landed, it gripped the surface, remained fixed on the outer edge of the disk at a distance R from the center, and set it into rotation. The sketch indicates the situation The mass of the mouse is m = 0.10 kg, the radius of the disk is R = 0.20 m, and the rotational inertia of the disk is I = 0.0080 kg· $m to the power of 2 end exponent$ . The speed of the mouse, just before it landed on the disk is $V subscript O end subscript$ = 1.5 m/s. The mouse, still searching for food, crept to the center of the disk (where r = 0). Find angular velocity of the disk plus mouse, when the mouse was at the center of the disk.

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