A horizontal curve on $a$ racing track is banked at a $45^o $ angle. When a vehicle goes around this curve at the curve’s safe speed (no friction needed to stay on the track), what is its centripetal acceleration?

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that  

Shown here are the velocities and acceleration vectors for a man in several different types of motion. In which case is the man slowing down and turning to the right

A ball of mass $0.1$ kg is suspended by a string. It is displaced through an angle of ${60^o}$ and left. When the ball passes through the mean position, the tension in the string is ........ $N$

Two bodies $A$ & $B$ rotate about an axis, such that angle $\theta_A$ (in radians) covered by first body is proportional to square of time, & $\theta_B$ (in radians) covered by second body varies linearly. At $t = 0, \theta \,A = \theta \,B = 0$. If $A$ completes its first revolution in $\sqrt \pi$ sec. & $B$ needs $4\pi \,sec$. to complete half revolution then; angular velocity $\omega_A : \omega_B$ at $t = 5\, sec$. are in the ratio

An aeroplane is flying with a uniform speed of $100\, m/s$ along a circular path of radius $100 m$. the angular speed of the aeroplane will be ......... $rad/sec$