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System of Particles and Rotational Motion

Rolling of a body on an inclined plane

As shown in figure, a uniform solid sphere rolls on a horizont

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Medium

Solving time: 3 mins

As shown in figure, a uniform solid sphere rolls on a horizontal surface at $20 m / s$ . It then rolls up the incline shown. What will be the value of $h$ , where the ball stops? (a) $28.6 m$ (b) $8.6 m$ (c) $6 m$ (d) $18.6 m$

Views: 5,123 students

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2008

Found 5 tutors discussing this question

Liam Discussed

As shown in figure, a uniform solid sphere rolls on a horizontal surface at

20 m / s

. It then rolls up the incline shown. What will be the value of

h

, where the ball stops?

(a)

28.6 m

(b)

8.6 m

(c)

6 m

(d)

18.6 m

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

The rotational and translational kinetic energy of the ball at the bottom will be changed to gravitational potential energy, when the sphere stops. We therefore write

(\frac{M v ^{2}}{2} + \frac{l ω ^{2}}{2})_{s t a r t} = (M g h)_{e n d}

For a solid sphere,

I = \frac{2 M r ^{2}}{5}

Also,

ω = \frac{V}{r}

. Then, above equation becomes

\frac{1}{2} M v^{2} + \frac{1}{2} (\frac{2}{5} M r^{2}) (\frac{v}{r})^{2} = M g h

\frac{1}{2} v^{2} + \frac{1}{5} v^{2} = (9.8) h

Using

v = 20 m / s

, gives

h = 28.6 m

. Note The answer does not depend upon the mass of the ball or the angle of the incline.

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Question Text	As shown in figure, a uniform solid sphere rolls on a horizontal surface at $20 m / s$ . It then rolls up the incline shown. What will be the value of $h$ , where the ball stops? (a) $28.6 m$ (b) $8.6 m$ (c) $6 m$ (d) $18.6 m$
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	12

As shown in figure, a uniform solid sphere rolls on a horizontal surface at $20 m / s$ . It then rolls up the incline shown. What will be the value of $h$ , where the ball stops? (a) $28.6 m$ (b) $8.6 m$ (c) $6 m$ (d) $18.6 m$

Text solutionVerified

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As shown in figure, a uniform solid sphere rolls on a horizontal surface at 20 m/s. It then rolls up the incline shown. What will be the value of h, where the ball stops? (a) 28.6 m (b) 8.6 m (c) 6 m (d) 18.6 m

Text solutionVerified

Questions from JEE Mains 2008 - PYQs

Practice questions from Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Practice questions from System of Particles and Rotational Motion in the same exam

Practice more questions from System of Particles and Rotational Motion

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As shown in figure, a uniform solid sphere rolls on a horizontal surface at $20 m / s$ . It then rolls up the incline shown. What will be the value of $h$ , where the ball stops? (a) $28.6 m$ (b) $8.6 m$ (c) $6 m$ (d) $18.6 m$