(B) For a particle to just 'loop the loop' in a vertical circle,the tension at the highest point must be zero $(T = 0)$.At the highest point,the centr

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(B) For a particle to just 'loop the loop' in a vertical circle,the tension at the highest point must be zero $(T = 0)$.At the highest point,the centripetal force is provided by gravity: $mg = \frac{mv^2}{r}$.Thus,$v = \sqrt{gr}$.Given $g = 10 \,m/s^2$ and $r = 2 \,m$,we have $v = \sqrt{10 \times 2} = \sqrt{20} \approx 4.47 \,m/s$.Therefore,the speed is $4.47 \,m/s$ and the tension is $0 \,N$.

Class 11 Physics Work, Energy, Power and Collision Vertical Circular Motion

Medium

$A$ particle of mass $200 \,g$ is moving in a circle of radius $2 \,m$. The particle is just 'looping the loop'. What are the speed of the particle and the tension in the string at the highest point of the circular path? (Take $g = 10 \,m/s^2$)

A
$4 \,m/s, 5 \,N$
B
$4.47 \,m/s, 0 \,N$
C
$2.47 \,m/s, 0 \,N$
D
$1 \,m/s, 0 \,N$

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Work, Energy, Power and Collision

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Vertical Circular Motion

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$A$ particle of mass $200 \,g$ is moving in a circle of radius $2 \,m$. The particle is just 'looping the loop'. What are the speed of the particle and the tension in the string at the highest point of the circular path? (Take $g = 10 \,m/s^2$)

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$A$ particle is rotated in a vertical circle by connecting it to a light rod of length $l$ and keeping the other end of the rod fixed. The minimum speed of the particle when the light rod is horizontal for which the particle will complete the circle is

$A$ bob of mass $M$ is suspended by a massless string of length $L$. The horizontal velocity $V$ at position $A$ is just sufficient to make it reach the point $B$. The angle $\theta$ at which the speed of the bob is half of that at $A$, satisfies:

$A$ pendulum consisting of a small sphere of mass $m$ suspended by an inextensible and massless string of length $l$ is made to swing in a vertical plane. If the breaking strength of the string is $2mg$,then the maximum angular amplitude of the displacement from the vertical can be ....... $^o$

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