A string of length $L$ is fixed at one end and carries a mass $M$ at the other end. The string makes $2/\pi$ revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is

An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at $x =+2\,m$, its velocity is $-4 \hat{ j }\, m / s$. The object's velocity $(v)$ and acceleration $(a)$ at $x =-2\,m$ will be

What is the value of linear velocity, if $\vec \omega = 3\hat i - 4\hat j + \hat k$ and $\vec r = 5\hat i - 6\hat j + 6\hat k$

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 of mass $200 \,g$ is moving in a circle of radius $2 \,m$. The particle is just 'looping the loop'. The speed of the particle and the tension in the string at highest point of the circular path are $\left(g=10 \,ms ^{-2}\right)$

A scooter is going round a circular road of radius $100 \,m$ at a speed of $10 \,m/s$. The angular speed of the scooter will be ......... $rad/s$