List of practice Questions

The range of a projectile projected at an angle of $ 15^\circ $ with the horizontal is $ 50 $ m. If the projectile is projected with the same velocity at an angle of $ 45^\circ $, then its range will be:

A rigid body rotates about a fixed axis with variable angular velocity $ \omega = \alpha - \beta t $ at time $ t $, where $ \alpha, \beta $ are constants. The angle through which it rotates before it stops is:

A projectile is projected with velocity of $ 40 $ m/s at an angle $ \theta $ with the horizontal. If $ R $ is the horizontal range covered by the projectile and after $ t $ seconds its inclination with horizontal becomes zero, then the value of $ \cot \theta $ is:
[Take, $ g = 10 $ m/s$ ^2 $]

The distance travelled by a particle starting from rest and moving with an acceleration $ \frac{4}{3} $ ms$^{-2} $, in the third second is:

A particle is moving in a straight line. The variation of position $ x $ as a function of time $ t $ is given as:
$ x = t^3 - 6t^2 + 20t + 15 $.
The velocity of the body when its acceleration becomes zero is:

The dimensions of the coefficient of self-inductance are:

The dimensional formula of latent heat is:

You measure two quantities as $ A = 1.0 \,m \pm 0.2 \,m $, $ B = 2.0 \,m \pm 0.2 \,m $. We should report the correct value for $ \sqrt{AB} $ as:

A parallel plate capacitor has 1 $\mu$F capacitance. One of its two plates is given $+2 \mu C$ charge and the other plate, $+4 \mu C$ charge. The potential difference developed across the capacitor is:

A charge particle moving in magnetic field $ B $, has components of velocity along $ B $ as well as perpendicular to $ B $. The path of the charge particle will be:

A body of mass $M$ at rest explodes into three pieces, in the ratio of masses 1:1:2. Two smaller pieces fly off perpendicular to each other with velocities of 30 m/s and 40 m/s respectively. The velocity of the third piece will be:

A charge particle moving in magnetic field $ B $, has components of velocity along $ B $ as well as perpendicular to $ B $. The path of the charge particle will be:

A body of mass $M$ at rest explodes into three pieces, in the ratio of masses 1:1:2. Two smaller pieces fly off perpendicular to each other with velocities of 30 m/s and 40 m/s respectively. The velocity of the third piece will be:

Five charges $ +q, +5q, -2q, +3q $ and $ -4q $ are situated as shown in the figure. The electric flux due to this configuration through the surface S is:

Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is:

The waves emitted when a metal target is bombarded with high energy electrons are:

When unpolarized light is incident at an angle of 60° on a transparent medium from air, the reflected ray is completely polarized. The angle of refraction in the medium is:

A heavy box of mass 50 kg is moving on a horizontal surface. If the coefficient of kinetic friction between the box and the horizontal surface is 0.3, then the force of kinetic friction is:

Two light beams of intensities in the ratio of 9:4 are allowed to interfere. The ratio of the intensity of maxima and minima will be:

If $ \mathbf{A} = 4\hat{i} + 3\hat{j} $ and $ \mathbf{B} = 3\hat{i} + 4\hat{j} $, then the cosine of the angle between $ \vec{A} $ and $ \vec{A} + \vec{B} $ is:

The refractive index $ \mu $ of the material of a prism is given by: % Formula for Refractive Index \[ \mu = \frac{\sin \left( \frac{A + \delta_m}{2} \right)}{\sin \left( \frac{A}{2} \right)} \] where $ A $ is the apex angle of the prism and $ \delta_m $ is the angle of minimum deviation.

Magnetic field at the centre of a circular coil of radius $ r $, through which a current $ I $ flows is:

The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately:

For a group of positive charges, which of the following statements is correct?

A bob of mass $ m $ is suspended by a light string of length $ L $. It is imparted a minimum horizontal velocity at the lowest point A such that it just completes half a circle, reaching the topmost position B. The ratio of kinetic energies $\left(\frac{K.E.}{K.E.}\right)_A $, $\text{to}$, $\left(\frac{K.E.}{K.E.}\right)_B$ is: