SATHEE: Rotational Motion Question 138

Rotational Motion Question 138

Question: A small solid sphere of radius $r$ rolls down an incline without slipping which ends into a vertical loop of radius $R$ . Find the height above the base so that it just loops the loop

Options:

A) $\frac{5}{2} R$

B) $\frac{5}{2} (R - r)$

C) $\frac{25}{10} (R - r)$

D) $\frac{27}{10} R - \frac{17 r}{10}$

Show Answer

Answer:

Correct Answer: D

Solution:

[d]The minimum velocity at P, top of the loop, should be

$v = \sqrt{g (R - r)}$ , if the sphere keeps on rolling at top

$v = ω R$

$m g h = \frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2} + m g (2 R - r)$

$= \frac{1}{2} m g (R - r) + \frac{1}{2} (\frac{2}{5}) m R^{2} 2 ω^{2} + m g (2 R - r)$

$= \frac{7}{10} m g (R - r) + m g (2 R - r)$

$ω R = v = \sqrt{g (R - r)}$

$= \frac{m g}{10} (27 R - 17 r) o r h = \frac{1}{10} (27 R - 17 r)$

Rotational Motion Question 138

Question: A small solid sphere of radius $r$ rolls down an incline without slipping which ends into a vertical loop of radius $R$ . Find the height above the base so that it just loops the loop

Options:

Answer:

Solution:

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Rotational Motion Question 138

Question: A small solid sphere of radius r rolls down an incline without slipping which ends into a vertical loop of radius R . Find the height above the base so that it just loops the loop

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: A small solid sphere of radius $r$ rolls down an incline without slipping which ends into a vertical loop of radius $R$ . Find the height above the base so that it just loops the loop