Question

A stone of mass m tied to the end of a string revolves in a vertical circle of radius R. The net forces at the lowest and highest points of the circle directed vertically downwards are:

Lowest Point Highest Point

• A. $\mathrm { mg } - \mathrm { T } _ { 1 }$ $\mathrm { mg } + \mathrm { T } _ { 2 }$
• B. $\mathrm { mg } + \mathrm { T } _ { 1 }$ $\mathrm { mg } - \mathrm { T } _ { 2 }$
• C. $\mathrm { mg } + \mathrm { T } _ { 1 } - \left( \frac { \mathrm { mv } _ { 1 } ^ { 2 } } { \mathrm { R } } \right)$ $\mathrm { mg } - \mathrm { T } _ { 2 } + \left( \frac { \mathrm { mv } _ { 2 } ^ { 2 } } { \mathrm { R } } \right)$
• D. $\mathrm { mg } - \mathrm { T } _ { 1 } - \left( \frac { \mathrm { mv } _ { 1 } { } ^ { 2 } } { \mathrm { R } } \right)$ $\mathrm { mg } + \mathrm { T } _ { 2 } + \left( \frac { \mathrm { mv } _ { 2 } ^ { 2 } } { \mathrm { R } } \right)$ $\mathrm { T } _ { 1 }$ and $\mathrm { v } _ { 1 }$ denote the tension and speed at the lowest point. $\mathrm { T } _ { 2 }$ and $v _ { 2 }$ denote corresponding values at the highest point :

Answer 1

Answer: (A)

$\mathrm { mg } - \mathrm { T } _ { 1 }$ $\mathrm { mg } + \mathrm { T } _ { 2 }$

Answer 2

At the lowest point, mg acts downwards and $T _ { 1 }$ upwards so that net force $= m g - T _ { 1 }$

At the highest point, both mg and $T _ { 2 }$ act downwards so that net force $= m g + T _ { 2 }$

Hence option (1) is correct