For the following questions answer them individually
A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle $$\theta$$, the spot of the light is found to move through a distance y on the scale. The angle $$\theta$$ is given by
An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current ‘I’ along the same direction is shown in Fig. Magnitude of force per unit length on the middle wire ‘B’ is given by
Young’s double slit experiment is first performed in air and then in a medium other than air. It is found that $$8^{th}$$ bright fringe in the medium lies where $$5^{th}$$ dark fringe lies in air. The refractive index of the medium is nearly
A spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is $$k'$$. Then they are connected in parallel and force constant is $$k"$$. Then $$k' : k"$$ is
A thin prism having refracting angle $$10^\circ$$ is made of glass of refractive index 1.42. This prism is combined with another thin prism of glass of refractive index 1.7. This combination produces dispersion without deviation. The refracting angle of second prism should be
A gas mixture consists of 2 moles of $$O_2$$ and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is
Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take g constant with a value
$$10 m/s^2$$. The work done by the (i) gravitational force and the (ii) resistive force of air is
The x and y coordinates of the particle at any time are $$x = 5t - 2t^2$$ and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2 s is
Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities $$\omega_1 and \omega_2.$$ They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is