SATHEE: Rotational Motion Question 81

Rotational Motion Question 81

Question: The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle $θ$ without slipping and slipping down the incline without rolling is

Options:

A) 5 : 7

B) 2 : 3

C) 2 : 5

D) 7 : 5

Show Answer

Answer:

Correct Answer: A

Solution:

A solid sphere rolling without slipping down an inclined plane In this case, $a_{1} = \frac{g \sin θ}{1 + \frac{k^{2}}{R^{2}}} = \frac{g s i n θ}{1 + \frac{(2 / 5) R^{2}}{R^{2}}}$

$[∴ f o r s o l i d s p h e r e, K^{2} = \frac{2}{5} R^{2}]$

$= \frac{g \sin θ}{7 / 5}$

$\Rightarrow$ $a_{1} = \frac{5}{7} g \sin θ$

For a sphere slipping down an inclined plane

$\Rightarrow$ $a_{2} = g \sin θ$

$\Rightarrow$ $\frac{a_{1}}{a_{2}} = \frac{5 / 7 g \sin θ}{g \sin θ}$

$\Rightarrow$ $\frac{a_{1}}{a_{2}} = \frac{5}{7}$

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Rotational Motion Question 81

Question: The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle θ without slipping and slipping down the incline without rolling is

Options:

Answer:

Solution:

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Question: The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle $θ$ without slipping and slipping down the incline without rolling is