Question

A stone of mass 1000 g tied to a light string of length 10/3 m is whirling in a vertical circle. If the ratio of the maximum tension to minimum tension is 4 and g = 10 ms^-2_, then speed of stone at the highest point of circle is

• A. 20 ms^-1
• B. 10/√3 ms^-1
• C. 5√3ms^-1
• D. 10 ms^-1

Answer 1

Answer: (D)

10 ms^-1

Answer 2

T_max= $\frac { \mathrm { mv } _ { 1 } ^ { 2 } } { \mathrm {~L} } + \mathrm { mg }$

and T_min = $\frac { \mathrm { mv } _ { \mathrm { h } } ^ { 2 } } { \mathrm {~L} } - \mathrm { mg }$

Then

= $\frac { v _ { 1 } ^ { 2 } + g L } { v _ { h } ^ { 2 } - g L }$ …………. (i)

Using v² – u² = 2aS, we get

v_h² - v_l² = - 2g(2L) = -4gL

or v_l² = v_h² + 4gL

Then from (i) $\frac { \mathrm { T } _ { \max } } { \mathrm { T } _ { \min } } = \frac { \mathrm { v } _ { \mathrm { h } } ^ { 2 } + 4 \mathrm { gL } + \mathrm { gL } } { \mathrm { v } _ { 1 } ^ { 2 } - \mathrm { gL } }$ or

4 = $\frac { \mathrm { v } _ { \mathrm { h } } ^ { 2 } + 5 \times 10 \times \frac { 10 } { 3 } } { \mathrm { v } _ { \mathrm { h } } ^ { 2 } - 10 \times \frac { 10 } { 3 } }$

or 3v_h² = 300 = or v_h = 10 ms^-1