JEE Physics 2023 Question with Solution

Given: mass of stone $m = 1 \, \text{kg}$, string length $r = 1 \, \text{m}$, maximum tension $T = 400 \, \text{N}$.

Find: the maximum linear velocity of the stone without breaking the string.

At the limiting condition, the maximum velocity occurs when the centripetal force equals the maximum tension in the string.

Setting centripetal force equal to tension:

Substitute the given values:

Therefore, the maximum linear velocity is $20 \, \text{m/s}$. The solution states the correct option is B, but this value matches option A, so the source has an option-label discrepancy.

Given: the stone moves in a horizontal circle and the string can sustain at most $400 \, \text{N}$ tension.

Find: the highest possible speed before the string breaks.

The string provides the required centripetal force. Hence the largest allowed speed is obtained when the required centripetal force becomes exactly equal to the breaking tension.

With $m = 1 \, \text{kg}$ and $r = 1 \, \text{m}$:

Therefore, the correct numerical value is $20 \, \text{m/s}$, which corresponds to option A in the listed options.