Question 192: Centre of Mass and Rotational Motion

Question

A sphere of mass 2 kg and 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?
![](https://imagex.cdn.examgoal.net/1kmlibf2w/c281c664-72af-4b95-a737-5c9431c5c6ec/ae2a8090-8b8e-11eb-8bc4-81bde7104d98/file-1kmlibf2x.jpg)

Accepted Answer

$a = {{g\sin 	heta } \over {1 + c}}$
$a = {{9.8\sin 30^\circ } \over {1 + {2 \over 5}}}$
a = 3.5 m/sec
2
Time of accent
V = u + at
0 = 1 $-$ 3.5 t
$t = {1 \over {3.5}}$ sec.
Time of decent
$t = {1 \over {3.5}}$ sec.
Total time $T = {2 \over {3.5}}$ = 0.57 sec.
![](https://imagex.cdn.examgoal.net/1kpk59ftl/67b2c7d3-9055-4286-a46b-08598e7b8934/7deda490-c633-11eb-8f69-79d81b6078c9/file-1kpk59ftm.png)

Answer

0.60 s

Answer

0.52 s

Answer

0.80 s

Answer

0.57 s

Centre of Mass and Rotational Motion

A sphere of mass 2 kg and 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?

Choose the correct answer: