A force $\vec F$ acts on a particle having position vector $\vec r$ (with respect to origin). It produces a torque $\vec \tau $ about origin, choose the correct option
$\vec r.\vec \tau > 0$ and $\vec F.\vec \tau < 0$
$\vec r.\vec \tau = 0$ and $\vec F.\vec \tau = 0$
$\vec r.\vec \tau = 0$ and $\vec F.\vec \tau \ne 0$
$\vec r.\vec \tau \ne 0$ and $\vec F.\vec \tau = 0$
If the earth were to suddenly contract to $1/n^{th}$ of its present radius without any change in its mass, the duration (in $hrs.$ ) of the new day will be nearly
A mass $‘m’$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?
A solid sphere is rolling on a frictionless surface, shown in figure with a translational velocity $v\,\,m/s.$ If it is to climb the inclined surface then $v$ should be
Three particles each of mass $m$ are placed at the corners of equilateral triangle of side $l$
Which of the following is lare correct?
Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant, then the speed of centre of mass of the system will be