$A$ $500 \,kg$ car takes a round turn of radius $50 \,m$ with a velocity of $36 \,km/h$. The centripetal force is (in $\,N$)

If a stone of mass $0.5 \ kg$ tied to one end of a wire is whirled in a circular path of radius $2 \ m$ with a speed $40 \ rev/min$ in a horizontal plane,then the tension in the wire is nearly (in $N$)

$A$ small disc is placed on the top of a smooth hemisphere of radius $R$. The smallest horizontal velocity $V$ that should be imparted to the disc so that it leaves the hemisphere surface immediately is (there is no friction):

$A$ particle of mass $M$ moves with constant speed along a circular path of radius $r$ under the action of a force $F$. Its speed is

When a vehicle of mass $m$ is moving with a velocity $v$ over a concave over-bridge of radius of curvature $r$,the thrust on the road at the lowest point on the bridge will be

One end of a massless spring of spring constant $k$ and natural length $l_{0}$ is fixed,while the other end is connected to a small object of mass $m$ lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity $\omega$ about an axis passing through the fixed end,then the elongation of the spring will be