Question

Assertion (A): To make a body to move along a vertical circle, its critical speed at a point is independent of mass of body
Reason (R) : When a body is rotated along a vertical circle with uniform speed then the sum of its kinetic energy and potential energy is constant at all positions.

Answer 1

Answer:

The critical speed of the body at the topmost point is equal to

gR

i.e v=

gR

Let the velocity of the body when the string is horizontal be v

2

Using work-energy theorem : W=ΔK.E

∴ mgR=

2

1

mv

2

2

−

2

1

mv

2

OR mgR=

2

1

mv

2

2

−

2

1

m(gR) ⟹v

2

2

=3gR

Centripetal acceleration a

r

=

R

v

2

2

=3g

Answer 2

The assertion (A) is correct but the reason (R) is false.

Explanation:

Given:

Assertion (A): To make a body to move along a vertical circle, its critical speed at a point is independent of mass of body

Reason (R) : When a body is rotated along a vertical circle with uniform speed then the sum of its kinetic energy and potential energy is constant at all positions.

Solution:

When a body is rotating in a vertical circle the critical speed at various points is independent of the mass of the body

For example, if the radius of the circle is r (length of the string) then

Critical speed the lowest point $v=\sqrt{5gr}$

Critical speed the highest point $v=\sqrt{gr}$

Critical speed when the string is horizontal $v=\sqrt{3gr}$

When a body is rotating in a vertical circle with uniform speed then its kinetic energy will be constant since the speed is constant however its potential energy will keep on changing as the height of the body rotating in a vertical circle will keep on changing.

Therefore, The assertion (A) is correct but the reason (R) is false.

Hope this answer is helpful.

Know More:

Q: A bucket containing water is whirled in a vertical circle at arms length. Find the minimum speed at top to ensure that no water spills out. Also find corresponding angular speed. (Assume r = 0.75 m)(Ans : 2.711 m/s. 3.615 rad/s) .

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