In the circuit shown in the figure,the potential difference across the $4.5\,\mu F$ capacitor is ....... $V$.

The equation of a wave on a string of linear mass density $0.04 \, kg \cdot m^{-1}$ is given by: $y = 0.02 \, \sin \left[ 2\pi \left( \frac{t}{0.04} - \frac{x}{0.50} \right) \right]$. The tension in the string is ..... $N$.

$A$ polaroid is placed at $45^{\circ}$ to an incoming linearly polarized light of intensity $I_0$. The intensity of light passing through the polaroid after polarization would be:

Assume that a drop of liquid evaporates by decrease in its surface energy,so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is $T$,density of liquid is $\rho$ and $L$ is its latent heat of vaporization.

$A$ segment of wire vibrates with a fundamental frequency of $450 ~Hz$ under a tension of $9 ~kg-wt$. The tension at which the fundamental frequency of the same wire becomes $900 ~Hz$ is

In a playground,there is a merry-go-round of mass $120 \ kg$ and radius $4 \ m$. The radius of gyration is $3 \ m$. $A$ child of mass $30 \ kg$ runs at a speed of $5 \ m/s$ tangent to the rim of the merry-go-round when it is at rest and then jumps on it. Neglecting friction,find the angular velocity of the merry-go-round and child in $rad/s$.