List of practice Questions

Two soap bubbles of radius 2 cm and 4 cm, respectively, are in contact with each other. The radius of curvature of the common surface, in cm, is _______________.

A parallel-plate capacitor of capacitance 40µF is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant K = 2. Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are -

The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature \( R = 2 \, \text{m} \). Another car approaches him from behind with a uniform speed of 90 km/hr. When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the side view mirror is \( a \). The value of \( 100a \) is _____________ m/s\(^2\).

Given is a thin convex lens of glass (refractive index \( \mu \)) and each side having radius of curvature \( R \). One side is polished for complete reflection. At what distance from the lens, an object placed on the optic axis so that the image gets formed on the object itself.

Which of the following circuits represents a forward biased diode?
Which of the following circuits represents a forward biased diode?

The motion of an airplane is represented by the velocity-time graph as shown below. The distance covered by the airplane in the first 30.5 seconds is                km.

Match the List-I with List-II


Choose the correct answer from the options given below:

The electric field of an electromagnetic wave in free space is \[ \vec{E} = 57 \cos \left[7.5 \times 10^6 t - 5 \times 10^{-3} (3x + 4y)\right] \left( 4\hat{i} - 3\hat{j} \right) \, \text{N/C}. \] The associated magnetic field in Tesla is:
A spherical surface of radius of curvature \( R \), separates air from glass (refractive index = 1.5). The center of curvature is in the glass medium. A point object \( O \) placed in air on the optic axis of the surface, so that its real image is formed at \( I \) inside glass. The line \( OI \) intersects the spherical surface at \( P \) and \( PO = PI \). The distance \( PO \) equals:
A solid sphere of mass \( m \) and radius \( r \) is allowed to roll without slipping from the highest point of an inclined plane of length \( L \) and makes an angle of \( 30^\circ \) with the horizontal. The speed of the particle at the bottom of the plane is \( v_1 \). If the angle of inclination is increased to \( 45^\circ \) while keeping \( L \) constant, the new speed of the sphere at the bottom of the plane is \( v_2 \). The ratio of \( v_1^2 : v_2^2 \) is:

A particle is projected at an angle of \( 30^\circ \) from horizontal at a speed of 60 m/s. The height traversed by the particle in the first second is \( h_0 \) and height traversed in the last second, before it reaches the maximum height, is \( h_1 \). The ratio \( \frac{h_0}{h_1} \) is __________. [Take \( g = 10 \, \text{m/s}^2 \)]

The electric flux is \( \varphi = \alpha \sigma + \beta \lambda \) where \( \lambda \) and \( \sigma \) are linear and surface charge density, respectively, and \( \left( \frac{\alpha}{\beta} \right) \) represents

A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J, then the mass of the bullet is               grams. Given Data: Latent heat of fusion of lead = \(2.5 \times 10^4 \, \text{J kg}^{-1}\) and specific heat capacity of lead = 125 J kg\(^{-1}\) K\(^{-1}\).

A point particle of charge \( Q \) is located at \( P \) along the axis of an electric dipole 1 at a distance \( r \) as shown in the figure. The point \( P \) is also on the equatorial plane of a second electric dipole 2 at a distance \( r \). The dipoles are made of opposite charge \( q \) separated by a distance \( 2a \). For the charge particle at \( P \) not to experience any net force, which of the following correctly describes the situation?


 

Identify the valid statements relevant to the given circuit at the instant when the key is closed.
 


\( \text{A} \): There will be no current through resistor R.
\( \text{B} \): There will be maximum current in the connecting wires.
\( \text{C} \): Potential difference between the capacitor plates A and B is minimum.
\( \text{D} \): Charge on the capacitor plates is minimum.
Choose the correct answer from the options given below:

A sub-atomic particle of mass \( 10^{-30} \) kg is moving with a velocity of \( 2.21 \times 10^6 \) m/s. Under the matter wave consideration, the particle will behave closely like            (h = \( 6.63 \times 10^{-34} \) J.s)

Regarding self-inductance: \( \text{A} \): The self-inductance of the coil depends on its geometry.
\( \text{B} \): Self-inductance does not depend on the permeability of the medium.
\( \text{C} \): Self-induced e.m.f. opposes any change in the current in a circuit.
\( \text{D} \): Self-inductance is the electromagnetic analogue of mass in mechanics.
\( \text{E} \): Work needs to be done against self-induced e.m.f. in establishing the current.
Choose the correct answer from the options given below:
Consider a circular disc of radius 20 cm with center located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of the center of mass of the residual or remaining disc from the origin will be:
A light hollow cube of side length 10 cm and mass 10g, is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is \( y \pi \times 10^{-2} \) s, where the value of \( y \) is:
(Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \), density of water = \( 10^3 \, \text{kg/m}^3 \))
Consider a moving coil galvanometer (MCG):
A : The torsional constant in moving coil galvanometer has dimensions \( [ML^2 T^{-2}] \)
B : Increasing the current sensitivity may not necessarily increase the voltage sensitivity.
C : If we increase the number of turns (N) to its double (2N), then the voltage sensitivity doubles.
D : MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with the galvanometer.
E : Current sensitivity of MCG depends inversely on the number of turns of the coil.
Choose the correct answer from the options given below:

Refer to the circuit diagram given in the figure, which of the following observations are correct?

 

Observations:

A. Total resistance of circuit is 6 Ω

B. Current in Ammeter is 1 A

C. Potential across AB is 4 Volts

D. Potential across CD is 4 Volts

E. Total resistance of the circuit is 8 Ω

Choose the correct answer from the options given below:

Given below are two statements:
Statement-I: The hot water flows faster than cold water.
Statement-II: Soap water has higher surface tension as compared to fresh water.
In the light of the above statements, choose the correct answer from the options given below:
A positive ion A and a negative ion B has charges \(6.67 \times 10^{-19}\) C and \(9.6 \times 10^{-10}\) C, and masses \(19.2 \times 10^{-27}\) kg and \(9 \times 10^{-27}\) kg respectively. At an instant, the ions are separated by a certain distance \(r\). At that instant, the ratio of the magnitudes of electrostatic force to gravitational force is \(P \times 10^{-13}\), where the value of \(P\) is:
Given a thin convex lens (refractive index \( \mu_2 \)), kept in a liquid (refractive index \( \mu_1, \mu_1<\mu_2 \)) having radii of curvature \( |R_1| \) and \( |R_2| \). Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?
What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness \( h \) in terms of the angle of incidence \( i \) and angle of refraction \( r \), if the glass slab is placed in air medium?