A particle of mass ${m}$ is suspended from a ceiling through a string of length $L$. The particle moves in a horizontal circle of radius $r$ such that ${r}=\frac{{L}}{\sqrt{2}}$. The speed of particle will be:

If the length of the second's hand in a stop clock is $3 \,cm$ the angular velocity and linear velocity of the tip is

If the equation for the displacement of a particle moving on a circular path is given by $(\theta) = 2t^3 + 0.5$, where $\theta$ is in radians and $t$ in seconds, then the angular velocity of the particle after $2\, sec$ from its start is    ......... $rad/sec$

A particle is tied to $20\, cm$ long string. It performs circular motion in vertical plane. What is the angular velocity of string when the tension in the string at the top is zero  ........ $rad/sec$

A particle moving in a circle of radius $R$ with uniform speed takes time $\mathrm{T}$ to complete one revolution. If this particle is projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it is equal to $4 R$. The angle of projection $\theta$ is then given by :

The driver of a car travelling at velocity $v$ suddenly see a broad wall in front of him at a distance $d$. He should