A solid sphere of mass 2 kg radius 0-5 m is rolling with an initial speed of 1 ms-1 goes up an inclined plane which makes an angle of 30- with the horizontal plane- without slipping- How long will the sphere take to return to the starting point A-

Acceleration of ball, a=gsinθ1+k^2R^2 where k is radius of gyration. For a solid sphere, k^2R^2=25 a=9.8sin30^∘1+25 a=3.5 m/sec^2 Time of ascent is given by v ...

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Standard XII

Physics

Projectile from a Height

A solid spher...

Question

A solid sphere of mass $2 kg$ radius $0.5 m$ is rolling with an initial speed of $1 {ms}^{- 1}$ goes up an inclined plane which makes an angle of $30^{\circ}$ with the horizontal plane, without slipping. How long will the sphere take to return to the starting point $A$ ?

0.80 s

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0.60 s

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0.52 s

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0.57 s

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Solution

The correct option is D $0.57 s$
Acceleration of ball, $a = \frac{g sin θ}{1 + \frac{k^{2}}{R^{2}}}$ where $k$ is radius of gyration.

For a solid sphere, $\frac{k^{2}}{R^{2}} = \frac{2}{5}$
$a = \frac{9.8 sin 30^{\circ}}{1 + \frac{2}{5}}$
$a = 3.5 {m/sec}^{2}$

Time of ascent is given by
$v = u + a t$
$0 = 1 - 3.5$ $t$
$t = \frac{1}{3.5} s$
Time of decent
$t = \frac{1}{3.5}$ $s e c$ .
Due to symmetry of motion.
Total time, $T = \frac{2}{3.5} = 0.57 s$

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A solid sphere of mass 2 kg radius 0.5 m is rolling with an initial speed of 1 ms−1 goes up an inclined plane which makes an angle of 30∘ with the horizontal plane, without slipping. How long will the sphere take to return to the starting point A?

The correct option is D 0.57 sAcceleration of ball, a=gsinθ1+k2R2 where k is radius of gyration. For a solid sphere, k2R2=25 a=9.8sin30∘1+25 a=3.5 m/sec2 Time of ascent is given by v=u+at 0=1−3.5 t t=13.5 s Time of decent t=13.5 sec. Due to symmetry of motion. Total time, T=23.5=0.57 s

A solid sphere of mass $2 kg$ radius $0.5 m$ is rolling with an initial speed of $1 {ms}^{- 1}$ goes up an inclined plane which makes an angle of $30^{\circ}$ with the horizontal plane, without slipping. How long will the sphere take to return to the starting point $A$ ?