Question

A hollow sphere and uniform sphere of the same mass m and radius R roll down an inclined plane from the same height H without slipping (Figure 9-59). Each is moving horizontally as it leaves the ramp. When the spheres | hit the ground, the range of the hollow sphere is L. Find the range L' of the uniform sphere. FIGURE Uniform Hollow sphere sphere

Answer 1

& Hollow sphere Moment of Inertia = 2%M82 solid sphere Moment of inertia = 3%98² using Energy Conservation Equation (i) for Hollow sphere Rolling i.e.co Pign a mv2 u ( Kit & Rotational energy mgh | mv² + 1 x 2 x m8²² { v=WR Rolling mgh = 1 mv² + 1 / m v2 { 1 + 2 = 312 = 36 mgh = {mv2 Jogh = Vus ,. Z het T be time taken to reach E ground, & this 'T' would be same for both solid & llow sphere as "=0 Range (L) = YXT = 156gh T =L -0 (ii) for solid sphere T=L aan mgh = 1 m 2 + 1 x 2 m v2 mgh = 1 m² + mv 2 s logh = Vss Range = 2 = Vss XT= slogh T=1 Replacing I from eq. 0 LEX