Question

A sphere of radius 0.625m is rotating about a horizontal axis with angular velocity 2πrad/s and is released from rest in vertical plane under gravity. The ratio of displacement of point P to that of point C after 0.5s from the start will be

Answer 1

@snowsurf

Answer 2

Options are
A).1:1
B).2:1
C).3:1
D).4:1
E).2√2:1

Answer 3

Is there a diagram for this problem?

Answer 4

The diagram is there..
Bt it is just a sphere rotating with speed w and point P is actually topmost point of sphere (O is centre)

Answer 5

@ganeshie8

Answer 6

You can try using conservation of energy to find the displacement.
\[PE=KE_T+KE_R\]

Where T and R are translation and rotation kinetic energy. The moment of inertia for a sphere is \[I=\frac{ 2}{ 5 }MR^2\]

I just look that value up. Most if not all physics books have a table for these.

Answer 7

Can't we simply do it in this way?
The displacement of point P in horizontal direction wud be due to the horizontal velocity it possess.
And since we know that there is no horizontal velocity for point C. So we just find out the displacement of the point P in horizontal direction using the relation s=vt (v=wR)
And the vertical displacement of both points would be same.
So net displacement of point P wud be
Sp=√Sx^2+Sy^2
abd that of C wud be Sc=Sy

Answer 8

First, you have to work out where point P is relative to C after 0.5 s.
It is very easy, since you know the sphere's rotation velocity.

Once this is done, everything becomes clear.

Answer 9

Sir that will be calculated in the sense that point P will be travelling horizontally too..
And point C wud not..
So we cn simply use this relation for thr displacement (relative)
Sx=vt
v wud be wr
Isn't it??

Answer 10

You must draw the system at both times.
First work out how much P will have rotated around C.

Answer 11

Work out angle rotated by P in 0.5 s.

Answer 12

Pi angle

Answer 13

Yes, so P starts at the top, and ends just below after 0.5 s.
So P will have travelled an extra distance of an exact diameter of the circle.

Answer 14

Okay so we got the displacement of point P to be 1/2gt^2+ 2R and that of C to be 1/2gt^2

Answer 15

Yes, definitely!