Question

A body of mass $m$ is rotated along a vertical circle of radius $r$ such that velocity of the body at a point of vertical circle is equal to critical velocity at that point then:
A) maximum change in K.E. during one revolution is $2mgr$
B) difference of maximum tension and minimum tension in the string is $6mg$
C) the ratio of minimum tension to maximum tension in the string is $1:6$
D) the ratio of minimum K.E. to maximum K.E. of the body is $1:5$

• A. A, B and C are true
• B. B, C and D are true
• C. A, C and D are true
• D. A, B and D are true

Answer 1

Answer: (D)

A, B and D are true

All velocities are critical
$1)\Delta K{E}_{max}=\frac{1}{2}m({\sqrt{5gr}}^2-{\sqrt{gr}}^2)$
$=2mgr$

$2)T_{max}=6mg$
$T_{min}=0$

$3)\frac{T_{min}}{T_{max}}\to 0(False)$

$4)\frac{K{E}_{max}}{K{E}_{min}}=\frac{V_{max}^2}{V_{min}^2}=\frac{5gr}{gr}=\frac{5}{1}$