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 :(a) 5 : 7(b) 2 : 3(c) 2 : 5(d) 7 : 5

Answer 1

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$\textsf{\pink{Q.}}$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 :

(a) 5 : 7

(b) 2 : 3

(c) 2 : 5

(d) 7 : 5

$\textsf{\pink{Ans.}}$

a.) 5:7

For slipping motion on an inclined plane the acceleration for a solid sphere making an angle θ  is given by = Aslipping = g sin Ф

For slipping motion on an inclined plane the acceleration for a solid sphere making an angle θ  is given by = Aslipping = g sin ФFor rolling motion of a sphere without slipping :

For slipping motion on an inclined plane the acceleration for a solid sphere making an angle θ  is given by = Aslipping = g sin ФFor rolling motion of a sphere without slipping :The acceleration of a sphere of mass m, radius r and moment of inertia I is -

For slipping motion on an inclined plane the acceleration for a solid sphere making an angle θ  is given by = Aslipping = g sin ФFor rolling motion of a sphere without slipping :The acceleration of a sphere of mass m, radius r and moment of inertia I is -Arolling = g sin Ф/ 1+l/mr²

For slipping motion on an inclined plane the acceleration for a solid sphere making an angle θ  is given by = Aslipping = g sin ФFor rolling motion of a sphere without slipping :The acceleration of a sphere of mass m, radius r and moment of inertia I is -Arolling = g sin Ф/ 1+l/mr²For a uniform sphere - l/mr² = 2/5

For slipping motion on an inclined plane the acceleration for a solid sphere making an angle θ  is given by = Aslipping = g sin ФFor rolling motion of a sphere without slipping :The acceleration of a sphere of mass m, radius r and moment of inertia I is -Arolling = g sin Ф/ 1+l/mr²For a uniform sphere - l/mr² = 2/5Thus, substituting -

For slipping motion on an inclined plane the acceleration for a solid sphere making an angle θ  is given by = Aslipping = g sin ФFor rolling motion of a sphere without slipping :The acceleration of a sphere of mass m, radius r and moment of inertia I is -Arolling = g sin Ф/ 1+l/mr²For a uniform sphere - l/mr² = 2/5Thus, substituting - Arolling/Aslipping = g sin Ф/ g sin Ф/ 1+l/mr² = g sin Ф/g sin Ф/1+2/5

For slipping motion on an inclined plane the acceleration for a solid sphere making an angle θ  is given by = Aslipping = g sin ФFor rolling motion of a sphere without slipping :The acceleration of a sphere of mass m, radius r and moment of inertia I is -Arolling = g sin Ф/ 1+l/mr²For a uniform sphere - l/mr² = 2/5Thus, substituting - Arolling/Aslipping = g sin Ф/ g sin Ф/ 1+l/mr² = g sin Ф/g sin Ф/1+2/5= 5/7

For slipping motion on an inclined plane the acceleration for a solid sphere making an angle θ  is given by = Aslipping = g sin ФFor rolling motion of a sphere without slipping :The acceleration of a sphere of mass m, radius r and moment of inertia I is -Arolling = g sin Ф/ 1+l/mr²For a uniform sphere - l/mr² = 2/5Thus, substituting - Arolling/Aslipping = g sin Ф/ g sin Ф/ 1+l/mr² = g sin Ф/g sin Ф/1+2/5= 5/7Thus, the ratio without slipping and slipping down the incline without rolling is 5:7

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Answer 2

Answer:

a) 5:7

Explanation:

For slipping motion on an inclined plane the acceleration for a solid sphere making an angle θ  is given by = Aslipping = g sin Ф

For rolling motion of a sphere without slipping :

The acceleration of a sphere of mass m, radius r and moment of inertia I is -

Arolling = g sin Ф/ 1+l/mr²

For a uniform sphere - l/mr² = 2/5

Thus, substituting -

Arolling/Aslipping = g sin Ф/ g sin Ф/ 1+l/mr² = g sin Ф/g sin Ф/1+2/5

= 5/7

Thus, the ratio without slipping and slipping down the incline without rolling is 5:7