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Chapter 12: Q. 69 (page 334)

A hollow sphere is rolling along a horizontal floor at 5.0 m/s when it comes to a 30o­ incline. How far up the incline does it roll before reversing direction?

Short Answer

Expert verified

It will go 4.25 m before reversing the direction.

Step by step solution

01

Given information

Velocity of hollow sphere = 5 m/s

Angle of inclination = 30o

02

Explanation

Lets draw the diagram as below to understand and solve the problem

Lets assume it reaches to the height h then

From the conservation of energy

12Mv2+12Iω2=Mgh

Substitute value I=23MR2andω=vR

We get ,

12Mv2+1223MR2vR2=Mgh12Mv2+13Mv2=Mgh

Cancel M and simplify

56v2=ghh=5v26g

Substitute the value to get height h,

h=5×5ms-126×9.8ms-2h=2.126m

From trigonometric ratio L=hsinθ

on substitution we get

⇒L=2.126m0.5=4.25m

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