A car changes speed from $18\,km/h$ to $36\,km/h$ in $5\,s$. The diameter of its wheel is $0.8\,m$ . The angular acceleration of the wheel is ........ $rad/s^2$

forceA particle moves with constant speed $v$ along a circular path of radius $r$ and completes the circle in time $T$. The acceleration of the particle is

A bob is whirled in a horizontal plane by means of a string with an initial speed of $\omega \mathrm{rpm}$. The tension in the string is $T$. If speed becomes $2 \omega$ while keeping the same radius, the tension in the string becomes:

A particle moves so that its position vector is given by $\overrightarrow {\;r} = cos\omega t\,\hat x + sin\omega t\,\hat y$ , where $\omega$ is a constant.  Which of the following is true?  

Two bodies of mass $10 \,kg$ and $5 \,kg$ moving in concentric orbits of radii $R$ and $r$ such that their periods are the same. Then the ratio between their centripetal acceleration is

A particle is moving in a circular path. The acceleration and momentum vectors at an instant of time are $\vec{a}=2 \hat{i}+3 \hat{j} m / s ^2$ and $\overrightarrow{ p }=6 \hat{ i } + 4 \hat{ j } kgm /$ $s$. Then the motion of the particle is