$A$ bullet of mass $10\,g$ moving horizontally with a velocity of $400\,m/s$ strikes a wooden block of mass $2\,kg$ which is suspended by a light inextensible string of length $5\,m$. As a result,the centre of gravity of the block is found to rise a vertical distance of $10\,cm$. The speed of the bullet after it emerges out horizontally from the block will be ............... $m/s$.

$A$ ray of light of intensity $I$ is incident on a parallel glass-slab at a point $A$ as shown in the figure. It undergoes partial reflection and refraction. At each reflection,$25\%$ of the incident energy is reflected. The rays $AB$ and $A'B'$ undergo interference. The ratio ${I_{\max }}/{I_{\min }}$ is (in $: 1$)

$A$ body of mass $5 \ kg$ makes an elastic collision with another body at rest and continues to move in the original direction after the collision with a velocity equal to $\frac{1}{10}$th of its original velocity. Then the mass of the second body is (in $kg$)

Two capacitors $C_1$ and $C_2 = 2C_1$ are connected in a circuit with a switch $S$ and a resistor $R$ as shown in the figure. Initially,the switch is open and $C_1$ holds charge $Q$. The switch is closed. At steady state,the charge on each capacitor will be

$A$ vibrating string of certain length $l$ under a tension $T$ resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length $75\, cm$ inside a tube closed at one end. The string also generates $4\, beats$ per second when excited along with a tuning fork of frequency $n$. Now when the tension of the string is slightly increased,the number of beats reduces to $2\, per second$. Assuming the velocity of sound in air to be $340\, m/s$,the frequency $n$ of the tuning fork in $Hz$ is

The angle between the lines whose direction cosines are given by the equations $l^2+m^2-n^2=0$ and $l+m+n=0$ is