A ball of mass \( m \) moving at a speed \( v \) makes a head-on collision with an identical ball at rest. The kinetic energy at the balls after the collision is \( \frac{3}{4} \) of the original. What is the coefficient of restitution?
Two coherent point sources \( S_1 \) and \( S_2 \) vibrating in phase emit light of wavelength \( \lambda \). The separation between them is \( 2\lambda \). The light is collected on a screen placed at a distance \( D \gg \lambda \) from the slit \( S_1 \) as shown. The minimum distance, so that intensity at \( P \) is equal to intensity at \( O \), is:
The resistance \( R \) of a conductor varies with temperature \( t \) as shown in the figure. If the variation is represented by \( R_t = R_0 \left( 1 + \alpha t + \beta t^2 \right) \), then:
A capacitor of capacitance 5 µF is connected as shown in the figure. The internal resistance of the cell is 0.5 Ω. The amount of charge on the capacitor plate is:
A block of mass \( m \) is in contact with the cart C as shown in the figure. The coefficient of static friction between the block and the cart is \( \mu \). The acceleration \( a \) of the cart that will prevent the block from falling satisfies:
The bob of a pendulum is released from a horizontal position A as shown in the figure. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lower most point B, given that it dissipated 5% of its initial energy against air resistance?
A glass prism ABC (refractive index 1.5), immersed in water (refractive index \( \frac{4}{3} \)). A ray of light is incident normally on face AB. If it is totally reflected at face AC, then