Question

A particle of mass m just complete the vertical circular motion derive the expression for difference in tension at highest and lowest point

Answer 1

We consider a particle of mass m is performing vertical circular motion of a circle of radius r.

at highest position, weight and tension in string both are along downward direction.

now, at the highest position,

T + mg = mv²/r .........(1)

here, v = √(gh) it is velocity at uttermost position in case of string.

so, T + mg = mg = 0

again, at lowermost position, weight and tension in string both are in opposite directions. tension acts radially inward while weight radially outward.

now , at the lowermost position,

T' - mg = mv'²/r ........(2)

here, v = √(5gh), it is velocity at Lowest position in case of string.

so, T' - mg = 5mgh , T' = 6mg

now, difference in tension at lowest and uttermost point for a particle performing vertical circular motion = T' - T = 6mg.

Answer 2

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