Question

A car is moving with uniform speed over a cicular bridge of radius R which subtends an angle of $90$ at its centre. Find the minimum possible speed so that the car cross the bridge without losing the contact ant where.

Answer 1

As the car is moving with a uniform speed then $v_1=v_2$ where $v_1$ and $v_2$ are the speed of the car at an angle ${180}^0$ and

${90}^0$ with respect to the center of the circular motion.

Now the magnitude of change in velocity of the car at an angle ${90}^0$

$=\sqrt{v_1^2+v_2^2-2v_1{v}_2\cos \theta }$

$=\sqrt{2}v$

Thus the minimum speed of the car must $\sqrt{2}$ times the speed of the car