List of practice Questions

A truck moving at a constant speed of 72 km/h enters a curved path of radius of curvature measuring 120 m. It's total acceleration is:
Two planets \( A \) and \( B \) have radii \( R \) and \( 1.5R \), and densities \( \rho \) and \( \frac{\rho}{2} \) respectively. The ratio of acceleration due to gravity at the surface of \( B \) to \( A \) is:
In a Rutherford scattering experiment, when a projectile of charge \( Z_1 \) and mass \( M_1 \) approaches a target nucleus of charge \( Z_2 \) and mass \( M_2 \), the distance of closest approach is \( r_0 \). The energy of the projectile is:
If \( m \) is magnetic moment and \( B \) is the magnetic field, then the torque is given by:
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:
A magnetic field does not interact with:
Find the pole strength of a magnet of length 2 cm, if the magnetic field strength \( B \) at distance 10 cm from the centre of a magnet on the axial line of the magnet is \( 10^{-4} \, \text{T} \).
The radius of the current carrying circular coil is doubled keeping the current passing through it the same. Then the ratio of the magnetic field produced at the centre of the coil before the doubling of the radius to the magnetic field after doubling of the radius is:
The properties of a material required to make permanent magnets are
A charged particle is moving in a uniform magnetic field \( \mathbf{B} = 2\hat{i} + 3\hat{j} \) T. If it has an acceleration of \( \mathbf{a} = \alpha\hat{i} - 4\hat{j} \) m/s², then the value of \( \alpha \) will be:
A conducting loop of radius \( \frac{10}{\sqrt{\pi}} \) cm is placed perpendicular to a uniform magnetic field of 0.5T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25s is:
The free space inside a current carrying toroid is filled with a material of susceptibility \( \chi = 2 \times 10^{-2} \). The percentage increase in the value of magnetic field inside the toroid will be:
For a given pair of transparent media, the critical angle for which colour is maximum?
An equiconvex lens made of glass of refractive index \(\frac{3}{2}\) has focal length f in air. It is completely immersed in water of refractive index \(\frac{4}{3}\). The percentage change in the focal length is
When light propagates through a given homogeneous medium, the velocities of
Pick the correct answer from the following two statements:
(a) Virtual image can be seen with the eyes.
(b) Virtual image can be captured on the screen.
The colour which has the highest critical angle of incidence is
The magnifying power of a telescope with tube length 60 cm is 5. Then the focal length of its eye piece is:
A dielectric of dielectric constant $ K $ is introduced such that half of its area of a capacitor of capacitance $ C $ is occupied by it. The new capacity is
When $ 10^{19} $ electrons are removed from a neutral metal plate, the electric charge on it is
If A and B are two matrices such that AB=B and BA=A then A2 + B2 =
State and prove the principle of conservation of angular momentum.
Velocity constant for a first order reaction is \( 2 \times 10^{-3} \, \text{s}^{-1} \). The half-life period for this reaction is
Temperature of a reaction with an activation energy value of 15 kcal mol\(^{-1}\) is increased from 300 K to 310 K. If the value of the ideal gas constant (R) is 1.9872 cal mol\(^{-1}\) K\(^{-1}\), the ratio of the reaction rate constants \(\left(\frac{k_{310}}{k_{300}}\right)\) (rounded off to two decimal places) is ____________.
Answer the following questions:
What is the value of resistance for an ideal voltmeter?