Question

The difference in tensions in the strings
at the lavest & highest points in path of a
particle of mass performing vectical circular motion is​

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.