Competitive Thinking

A body initially at rest and sliding along a frictionless track from a height $h$ (as shown in the figure) just completes a vertical circle of diameter $AB=D$. The height $h$ is equal to

A particle moves in a circle of radius $5 \mathrm{cm}$ with constant speed and time period $0.2\pi \mathrm{s}$. The acceleration of the particle is 
 

A uniform circular disc of radius $50 \mathrm{cm}$ at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of $2.0 \mathrm{rad} {\mathrm{s}}^{-2}$. Its net acceleration in $\mathrm{m} {\mathrm{s}}^{-2}$ at the end of $2.0 \mathrm{s}$ is approximately

A particle is moving with a uniform speed in a circular orbit of radius $R$ in a central force inversely proportional to the $n^{\text{th }}$ power of $R$. If the period of rotation of the particle is $T$, then 
 

A particle is moving in a circular path of radius $a$ under the action of an attractive potential $U=-\frac{k}{2{\mathrm{r}}^2}$. Its total energy is

A point object moves along an arc of a circle of radius $R$. Its velocity depends upon the distance covered $S$ as $V=K\sqrt{S}$, where, $K$ is a constant. If $\theta °$ is the angle between the total acceleration and tangential acceleration, then 

Two identical discs of the same radius $R$ are rotating about their axes in opposite directions with the same constant angular speed $\omega$. The discs are in the same horizontal plane. At time $t=0$, the points $P\text{ and} Q$ are facing each other as shown in the figure. The relative speed between the two points $P \text{and} Q \text{is} v_r$. As a function of time, it is best represented by

A wheel of circumference $C$ is at rest on the ground. When the wheel rolls forward through half a revolution, then the displacement of initial point of contact will be