$A$ car of mass $m$ is crossing a convex bridge of radius of curvature $R$ with speed $V$. At the highest point, the thrust (normal force) is ($g =$ gravitational acceleration).

$A$ particle rotates in a horizontal circle of radius $r$ in a conical funnel with speed $v$. The inner surface of the funnel is smooth. The height $h$ of the plane of the circle from the vertex of the funnel is (where $g$ is the acceleration due to gravity):

$A$ particle is moving with constant speed along a uniform helical path $(a)$ and a spiral path $(b)$ separately,as shown in the figure.

$A$ car is moving with high velocity when it takes a turn. $A$ force acts on it outwardly because of

If mass,speed,and radius of the circular path of a particle are increased by $100 \%$,then the necessary force required to maintain the circular path will have to be increased by (in $\%$)

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