List of practice Questions

An \( \alpha \)-particle of 10 MeV collides head-on with a copper nucleus (\( Z = 29 \)) and is deflected back. The minimum distance of approach between the centers of the two is:

A parallel plate air capacitor of capacitance \( C \) is connected to a cell of emf \( V \) and then disconnected from it. A dielectric slab of dielectric constant \( K \), which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?

A ball of radius \( r \) and density \( \rho \) falls freely under gravity through a distance \( h \) before entering water. The velocity of the ball does not change even on entering water. If the viscosity of water is \( \eta \), the value of \( h \) is given by:
\includegraphics[width=0.5\linewidth]{28.png}

For the circuit shown in the figure, the current through the inductor is \( 0.9A \) while the current through the condenser is \( 0.4A \). Then:

A planet in a distant solar system is 10 times more massive than Earth and its radius is 10 times smaller. Given that the escape velocity from Earth's surface is 11 km/s, the escape velocity from the planet’s surface would be:

Assertion :
The binding energy of the nucleus increases with the increase in atomic number.
Reason :
Heavier elements have a greater number of non-radioactive isotopes than radioactive isotopes.

If \( m \) is magnetic moment and \( B \) is the magnetic field, then the torque is given by:

A sinusoidal voltage of amplitude 25 V and frequency 50 Hz is applied to a half-wave rectifier using a P-N junction diode. No filter is used, and the load resistor is \( 1000\Omega \). The forward resistance \( R_f \) of the ideal diode is \( 10\Omega \). The percentage rectifier efficiency is:

A person aiming to reach the exactly opposite point on the bank of a stream is swimming with speed of \( 0.5 \) m/s at an angle of \( 120^\circ \) with the direction of flow of water. The speed of water in the stream is:

A square frame of side \( 10 \) cm and a long straight wire carrying current \( 1A \) are in the plane of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of \( 10 \) m/s (see figure). The induced EMF at the time the left arm of the frame is at \( x = 10 \) cm from the wire is:

A force \( \mathbf{F} = \alpha \hat{i} + 3 \hat{j} + 6 \hat{k} \) is acting at a point \( \mathbf{r} = 2 \hat{i} - 6 \hat{j} - 12 \hat{k} \). The value of \( \alpha \) for which angular momentum about the origin is conserved is:

A given ray of light suffers minimum deviation in an equilateral prism \( P \). Additional prisms \( Q \) and \( R \) of identical shape and of the same material as \( P \) are now added as shown in the figure. The ray will now suffer:
\includegraphics[width=0.5\linewidth]{31.png}

Consider an electric field \( \mathbf{E} = E_0 \hat{x} \), where \( E_0 \) is a constant. The flux through the shaded area (as shown in the figure) due to this field is:

An electron (mass = \( 9 \times 10^{-31} \) kg, charge = \( 1.6 \times 10^{-19} \) C) moving with a velocity of \( 10^6 \) m/s enters a magnetic field. If it describes a circle of radius \( 0.1 \) m, then the strength of the magnetic field must be:

A car moves at a speed of \( 20 { m/s} \) on a banked track and describes an arc of a circle of radius \( 40\sqrt{3} \) m. The angle of banking is: (Take \( g = 10 { m/s}^2 \))

A convex lens has power \( P \). It is cut into two halves along its principal axis. Further, one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in figure). Choose the incorrect option for the reported pieces.
\includegraphics[width=0.5\linewidth]{27.png}

A and B are two metals with threshold frequencies \( 1.8 \times 10^{14} \) Hz and \( 2.2 \times 10^{14} \) Hz. Two identical photons of energy \( 0.825 \) eV each are incident on them. Then photoelectrons are emitted in (Take \( h = 6.6 \times 10^{-34} \) Js):

The force between two short bar magnets with magnetic moments \( M_1 \) and \( M_2 \) whose centers are \( r \) meters apart is 8 N when their axes are in the same line. If the separation is increased to \( 2r \), the force between them is reduced to:

The half-life of radioactive radon is 3.8 days. The time at the end of which \(\frac{1}{20}th\) of the Radon sample will remain undecayed is (given log₁₀^e=0.4343)