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System Of Particles And Rotational Motion

Question

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A tangential force acting on the top of sphere of mass m kept on a rough horizontal place as shown in figure

If the sphere rolls without slipping, then the acceleration with which the centre of sphere moves, is

$\frac{10 F}{7 m}$

$\frac{F}{2 m}$

$\frac{3 F}{7 m}$

$\frac{7 F}{2 m}$

Solution

$\frac{10 F}{7 m}$

Let a be the acceleration of centre of sphere. The angular acceleration about the centre of the sphere is $α = \frac{θ}{r}$ , as there is no slipping.

For the linear motion of the centre

f + F = ma .....(i)

and for the rotational motion about the centre

Fr - fr = I α

= $(\frac{2}{5} {mr}^{2}) (\frac{a}{r})$

⇒ F - f = $\frac{2}{5} ma$ ....(ii)

From Eqs. (i) and (ii)

2F = $\frac{7}{5} ma$

⇒ a = $\frac{10 F}{7 m}$

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System Of Particles And Rotational Motion

A tangential force acting on the top of sphere of mass m kept on a rough horizontal place as shown in figure

If the sphere rolls without slipping, then the acceleration with which the centre of sphere moves, is

$\frac{10 F}{7 m}$

$\frac{F}{2 m}$

$\frac{3 F}{7 m}$

$\frac{7 F}{2 m}$

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For Daily Free Study Material Join wiredfaculty

System Of Particles And Rotational Motion

A tangential force acting on the top of sphere of mass m kept on a rough horizontal place as shown in figure If the sphere rolls without slipping, then the acceleration with which the centre of sphere moves, is 10 F7 m F2 m 3 F7 m 7 F2 m

Some More Questions From System of Particles and Rotational Motion Chapter

Angular momentum of the particle rotating with a central force is constant due to

Four point masses, each of value m, are placed at the corners of a square ABCD of side A. The moment of inertia through A and parallel to BD is

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A tangential force acting on the top of sphere of mass m kept on a rough horizontal place as shown in figure

If the sphere rolls without slipping, then the acceleration with which the centre of sphere moves, is

$\frac{10 F}{7 m}$

$\frac{F}{2 m}$

$\frac{3 F}{7 m}$

$\frac{7 F}{2 m}$