Question

A stone of mass 5 kg is tied to a string of length 10 m is whirled round in a horizontal circle. What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N?

• A. $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
• B. $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
• C. $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
• D. $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$

Answer 1

Answer: (C)

$20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$

Answer 2

Here $m = 5 \mathrm {~kg} , r = 10 \mathrm {~m} , T _ { \max } = 200 \mathrm {~N}$

As $T _ { \max } = \frac { m v _ { \max } ^ { 2 } } { r } \therefore v _ { \max } ^ { 2 } = \frac { T _ { \max } \times r } { m }$

$\therefore v _ { \max } ^ { 2 } = \frac { 200 \times 10 } { 5 } = 400 \Rightarrow v _ { \max } = 20 \mathrm {~ms} ^ { - 1 }$