$A$ particle of mass $m$ is moving in a circular path of radius $r$ in a plane. Its angular momentum is $L$. The value of the centripetal force acting on the particle is:

$A$ particle describes a horizontal circle of radius $r$ on the smooth surface of an inverted cone as shown. The height of the plane of the circle above the vertex is $h$. The speed of the particle should be

$A$ ball of mass $0.5 \ kg$ is attached to a string of length $50 \ cm$. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is $400 \ N$. The maximum possible value of angular velocity of the ball in $rad/s$ is:

$A$ train is moving towards north. At one place it turns towards north-east,here we observe that

$A$ body of mass $10 \,g$ is tied to a string of length $0.4 \,m$ and it is whirled in a horizontal plane with a speed of $6 \,m/s$. Then the tension in the string is (in $\,N$)

One end of a string of length $l$ is connected to a particle of mass $m$ and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $v$,the net force on the particle (directed towards the centre) is :
$(i) \; T$
$(ii) \; T - \frac{m v^{2}}{l}$
$(iii) \; T + \frac{m v^{2}}{l}$
$(iv) \; 0$
$T$ is the tension in the string. [Choose the correct alternative].