Question

show the total energy of a particle performing vertical circular motion is
conserved or constant ??​

Answer 1

Answer:

conserved

Explanation:

the answer is that is is conserved.

Answer 2

The total energy of a particle performing vertical circular motion is conserved or constant.

Proof : Let us take lowest point as frame of reference.

Given : V(lowest point) = √5gr, V(top point) = √gr and when string is horizontal V= √3gr

1. For lowest point, h=0

K.E = 1/2×mv^2 = 1/2×m×(√5gr)^2

= 1/2×m×5gr = 5/2×mgr

P.E = mg(0) = 0

T.E = K.E + P.E = 5/2×mgr + 0

= 5/2×mgr

2. For top point, h=2r

K.E = 1/2×m×(√gr)^2 = 1/2×mgr

P.E = mg(2r)

T.E = K.E + P.E = 1/2×mgr + mg(2r)

= 5/2×mgr

3. When string is horizontal, h=r

K.E = 1/2×m×(√3gr)^2 = 1/2×3mgr

= 3/2×mgr

P.E = mgr

T.E = K.E + P.E = 3/2×mgr + mgr

= 5/2×mgr

Hence proved that the total energy of a particle performing vertical circular motion is conserved or constant.