$A$ ball of mass $0.25 \, kg$ attached to the end of a string of length $1.96 \, m$ is moving in a horizontal circle. The string will break if the tension is more than $25 \, N$. The maximum speed with which the ball can be moved is .......... $m/s$.

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

$A$ car moving at a speed of $72 \; km/hr$ passes through a point $P$ on a curved road with a radius of $10 \; m$. The mass of the car is $500 \; kg$. Find the contact force (normal force) at point $P$ in $kN$. (Take $g = 10 \; m/s^2$)

Three particles of equal mass are tied to a string and rotated in a horizontal plane as shown. What is the ratio of tensions in the three parts of the string?

As shown in the figure, two equal masses hang on either side of a pulley at the same height from the ground. The mass on the right is given a horizontal speed $u$. After some time :-

$A$ car is moving on an overbridge of radius $R$ with a constant speed $v$. As the car is descending on the overbridge from point $B$ to $C$,the normal reaction on it due to the bridge: