List of practice Questions

A rectangular glass block of thickness 10 cm and refractive index 1.5 is placed over a small coin. A beaker is filled with water of refractive index 4/3 to a height of 10 cm and placed over the glass block. The apparent depth of coin when viewed at near normal incidence is:
A particle executes two simple harmonic motions along mutually perpendicular axes, given by \( x = A \sin(\omega_1 t) \) and \( y = B \cos(\omega_2 t) \) where \( A \neq B \) and \( \omega_1 = \omega_2 \). Which of the following best describes the resultant motion of the particle?
If a body is thrown vertically upwards from the surface of the earth with a speed equal to 75% of the escape speed from the surface of the earth, then the ratio of the maximum height reached by the body and the radius of the earth is:
A wire of weight W and area of cross-section A elongates under its own weight. If Y is the Young's modulus and \(\sigma\) is the Poisson's ratio of the material of the wire, then the fractional change in the radius of the wire is:
A capillary tube of inner radius 1.5 mm is dipped vertically in water. If the surface tension of water is \( 7 \times 10^{-2} \text{ Nm}^{-1} \), then the volume of the water that rises in the capillary tube is (\( g=10 \text{ ms}^{-2} \)):
Two semicircular rods AB and CD each of radius of curvature 14 cm and a straight rod BC of length 22 cm are connected in series. The three rods have equal area of cross-section and the thermal conductivities of the materials of the rods AB, BC and CD are in the ratio 1:2:3. In steady state, if the temperature difference between the ends of the middle rod BC is 30°C, then the temperature difference between the ends of the rods AB and CD are respectively:
If the temperature of a steel solid sphere of mass 4 kg and radius 5 cm is increased by 10°C then the increase in the moment of inertia of the sphere about its diameter is: (Coefficient of linear expansion of steel = \( 1.2 \times 10^{-5} \text{K}^{-1} \))
A body of mass 1 kg is attached to one end of a string of 1 m length. It is rotated in a vertical circle with a constant speed of \( 4 \text{ ms}^{-1} \). When the object is at the highest point of the vertical circle, tension in the string is (\( g=10 \text{ ms}^{-2} \)):
A body of mass 2 kg is thrown vertically upwards from the ground level with kinetic energy of 240 J. The kinetic energy of the body will become half at a height of (\( g=10 \text{ ms}^{-2} \)):
A person lifts 60 kg load to a vertical height of 30 m over a duration of 20 seconds. If the power of the man is 1323 W, the mass of the man is:
\( I_1 \) represents moment of inertia of a thin, uniform rod about an axis perpendicular to its length and passing through its centre of mass. The same rod is bent into the shape of a ring. If \( I_2 \) is moment of inertia of ring about an axis that is tangent to the ring and perpendicular to its plane, then \(\frac{I_1}{I_2}=\):
A particle is moving in a circular path with constant angular velocity. Its initial angular momentum is L. If the radius of the circle is tripled by keeping angular velocity same, the new angular momentum is:
The maximum kinetic energy of a pendulum executing simple harmonic motion is E. If the length of the pendulum is doubled and the amplitude of motion is halved, then the maximum kinetic energy of the pendulum is:
An object is sliding from the top of the smooth inclined plane of height \( h \) from rest and it just completes a vertical circle of diameter 20 cm. Then the minimum height \( h \) of smooth inclined plane is:
A body of mass 1 kg is attached to one end of a string of 1 m length. It is rotated in a vertical circle with a constant speed of \( 4 \text{ ms}^{-1} \). When the object is at the highest point of the vertical circle, tension in the string is (\( g=10 \text{ ms}^{-2} \)):
A body of mass 2 kg is thrown vertically upwards from the ground level with kinetic energy of 240 J. The kinetic energy of the body will become half at a height of (\( g=10 \text{ ms}^{-2} \)):
A person lifts 60 kg load to a vertical height of 30 m over a duration of 20 seconds. If the power of the man is 1323 W, the mass of the man is:
\( I_1 \) represents moment of inertia of a thin, uniform rod about an axis perpendicular to its length and passing through its centre of mass. The same rod is bent into the shape of a ring. If \( I_2 \) is moment of inertia of ring about an axis that is tangent to the ring and perpendicular to its plane, then \(\frac{I_1}{I_2}=\):
A particle is moving in a circular path with constant angular velocity. Its initial angular momentum is L. If the radius of the circle is tripled by keeping angular velocity same, the new angular momentum is:
Among the following differential equations, the equation having order 2 and degree 3 is:
The general solution of the differential equation \( \frac{dy}{dx} + y \tan x = - \tan x \log(\cos x) \) (\(0 < x < \pi/2\)) is:
For a particular wire of \( mass = (0.6 \pm 0.003) \) gm, \( radius = (0.50 \pm 0.01) \) cm, and \( length = (10.00 \pm 0.05) \) cm, the maximum percentage error in the measurement of its density is:
The three graphs represent acceleration Vs time for objects that have positive velocity at time \( t_1 \). Which graphs show the objects that move with increasing velocity for the entire time interval between \( t_1 \) and \( t_2 \)?
Two objects A and B are projected with same velocity at angles \( \theta \) and \( 90-\theta \) respectively with the horizontal. Then the ratio of maximum heights they reached \( \frac{H_A}{H_B} \) is:
A particle has initial velocity \( 2\hat{i} + 3\hat{j} \) \( ms^{-1} \) and acceleration \( 0.8\hat{i} + 0.6\hat{j} \) \( ms^{-2} \). Its velocity after 5 sec is (in \( ms^{-1} \)):