If the earth were to suddenly contract to $\frac {1}{n}^{th}$ of its present radius without any change in its mass the duration of the new day will be nearly
$\frac {24}{n}\,hr$
$24\,n\,hr$
$\frac {24}{n^2}\,hr$
$24\,n^2\,hr$
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
If the density of material of a circular plate and a square plate as shown is same, the centre of mass of the composite system will be
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
Two discs of moments of inertia $I_1$ and $I_2$ about their respective axes (normal to the disc and passing through the centre), and rotating with angular speed $\omega _1$ and $\omega _2$ are brought into contact face to face with their axes of rotation coincident. What is the loss in kinetic energy of the system in the process?
Five masses each of $2\, kg$ are placed on a horizontal circular disc, which can be rotated about a vertical axis passing through its centre and all the masses be equidistant from the axis and at a distance of $10\, cm$ from it. The moment of inertia of the whole system (in $gm-cm^2$ ) is: (Assume disc is of negligible mass)