Question 1

For an object in gravitational field, the gravitational potential is the same at two points A and B, but the gravitational field is not the same at these two points. Which one of the following stateme

Accepted Answer

The work done by the gravitational force on an object of mass m in moving it from point A to point B is given by W = - U = -m(V_B - V_A) = m(V_A - V_B), where V_A and V_B are the gravitational potentials at points A and B respectively. It is given that the gravitational potential is the same at points A and B, which means V_A = V_B. Substituting this into the work equation, we get W = m(V_A - V_A) = 0. The difference in the gravitational field at the two points does not affect the total work don

Question 2

A very large container consists of an ideal gas. The speed of sound in the gas is x. When the pressure of the gas is doubled while keeping the temperature constant, the speed of sound now becomes y. W

Accepted Answer

The speed of sound in an ideal gas is given by the formula v = R T M . Since the temperature T is kept constant and the gas remains the same, the values of , R, T, and M are all constant. Therefore, the speed of sound is independent of the pressure of the gas as long as the temperature is constant. Alternatively, using v = P , when the pressure P is doubled at constant temperature, the density also doubles, keeping the ratio P constant. Thus, the new speed of sound y is equal to the initial spee

Question 3

A constant power machine pulls a block on a smooth horizontal surface. Which one of the following correctly describes the relation between speed of the block (v) and time (t)?

Accepted Answer

Power is given by P = Fv Using Newton's second law, F = m dv dt Substituting this into the power equation: P = m ( dv dt )v v dv = P m dt Integrating both sides, assuming the block starts from rest: _ 0 ^ v v dv = _ 0 ^ t P m dt v^2 2 = P m t v = 2P m t Since P and m are constants, v t Answer: v t

Question 4

A ball is dropped from rest from height h above the ground in frame S (the Earth's frame). Another frame S' is moving upwards with constant speed u relative to the Earth. In frame S', the ball has ini

Accepted Answer

In frame S (Earth's frame): Initial velocity of the ball, v_ i = 0 Final velocity of the ball just before hitting the ground, v_ f = 2gh (downwards) Change in kinetic energy in frame S is: K_ S = 1 2 m v_ f ^2 - 1 2 m v_ i ^2 = 1 2 m (2gh) - 0 = mgh In frame S' (moving upwards with constant speed u): Initial velocity of the ball, v'_ i = u = v (downwards) Final velocity of the ball, v'_ f = 2gh + v (downwards) Change in kinetic energy in frame S' is: K_ S' = 1 2 m (v'_ f )^2 - 1 2 m (v'_ i )^2 K

Question 5

A pendulum of length L oscillates with an angular amplitude of = 60^ and time period T. Let T_0 = 2 L g be the time period for small angle of oscillations, where g is the acceleration due to gravity.

Accepted Answer

The restoring torque acting on the pendulum is = -mgL . The angular acceleration is = - g L . For small angular amplitudes, , which gives the time period T_0 = 2 L g . For a large angular amplitude ( = 60^ ), Due to the smaller restoring torque, the angular acceleration is reduced, which increases the time taken to complete an oscillation. The exact time period for large amplitudes is given by the series expansion T = T_0 ( 1 + 1 4 ^2 ( _0 2 ) + ). Since _0 = 60^ , the terms in the bracket are p

Question 6

A solid of mass m has temperature-dependent specific heat as C(T) = C_0 + T, where C_0 and are constants. The solid is heated from T_1 to T_2. Which one of the following is the correct expression for

Accepted Answer

The quantity of heat dQ required to raise the temperature of a mass m by dT is given by: dQ = m C(T) dT Substituting the given specific heat C(T) = C_0 + T: dQ = m (C_0 + T) dT Integrating both sides from T_1 to T_2: Q = _ T_1 ^ T_2 m (C_0 + T) dT Q = m [ C_0 T + T^2 2 ]_ T_1 ^ T_2 Q = m [ C_0 (T_2 - T_1) + 2 (T_2^2 - T_1^2) ] Using the identity T_2^2 - T_1^2 = (T_2 - T_1)(T_2 + T_1): Q = m (T_2 - T_1) [ C_0 + 2 (T_1 + T_2) ] Answer: Q = m(T_2 - T_1) [C_0 + 2 (T_1 + T_2) ]

Question 7

In a certain process, the relation between pressure (P) and volume (V), for an ideal gas, is given by PV^2 = constant . If the initial temperature is T_1 and the final temperature is T_2; and the init

Accepted Answer

The given process equation is PV^2 = constant . For an ideal gas, the equation of state is PV = nRT, which gives P = nRT V . Substituting the expression for P into the process equation: ( nRT V ) V^2 = constant T V = constant nR = constant This implies that T_1 V_1 = T_2 V_2. Rearranging the terms, we get: T_1 T_2 = V_2 V_1 Answer: T_1 T_2 = V_2 V_1

Question 8

An object is placed far beyond the centre of curvature of a concave mirror. The object then starts accelerating towards the mirror. Which one of the following is correct?

Accepted Answer

Using the mirror formula: 1 v + 1 u = 1 f Differentiating with respect to time t, we get the velocity of the image v_i in terms of the velocity of the object v_o: - 1 v^2 dv dt - 1 u^2 du dt = 0 v_i = - ( v u )^2 v_o = - f^2 (u-f)^2 v_o Since the object is moving towards the mirror, u is increasing (becoming less negative), so v_o > 0. This makes v_i To find the acceleration of the image a_i, we differentiate v_i with respect to t: a_i = dv_i dt = - f^2 (u-f)^2 a_o + 2f^2 (u-f)^3 v_o^2 Here, a_o

Question 9

A person jumps from a height on soft sand. Which one of the following is the correct reason for less likely injury to the person?

Accepted Answer

According to Newton's second law of motion, the average force exerted on a body is equal to the rate of change of momentum, F = p t . When a person jumps from a height onto soft sand, the sand yields under the person's weight. This increases the time of impact t for the person to come to rest. Since the change in momentum p remains the same (as the initial velocity just before impact and the final velocity of zero are unchanged), an increase in the impact time t results in a significant decrease

Question 10

One year at a planet is 8 times as large as compared to the one year at the Earth. Which one of the following is correct about the planet's orbit?

Accepted Answer

According to Kepler's third law of planetary motion, the square of the time period of revolution is directly proportional to the cube of the semimajor axis of the orbit. T^2 a^3 ( T_p T_e )^2 = ( a_p a_e )^3 Given that T_p = 8 T_e, substituting this value: (8)^2 = ( a_p a_e )^3 64 = ( a_p a_e )^3 a_p a_e = (64)^ 1/3 = 4 a_p = 4 a_e The semimajor axis of the planet's orbit is four times as compared to that of the Earth. Answer: The semimajor axis of the planet's orbit is four times as compared to

Question 11

A particle is moved from point X to point Y under a force field. The work done depends only on the initial and final speeds. Which one of the following is correct?

Accepted Answer

According to the work-energy theorem, the net work done on a particle by all forces equals the change in its kinetic energy. W_ net = K = 1 2 m(v_f^2 - v_i^2) Since kinetic energy depends only on the speed of the particle, the net work done depends only on the initial and final speeds. This holds true for any type of force, whether conservative or non-conservative, constant or variable. Answer: The net work equals the change in kinetic energy.

Question 12

A lightning rod with sharp tip reduces damage risk. Which one of the following is the primary reason for it?

Accepted Answer

A lightning rod has a sharp tip, which means the radius of curvature at the tip is very small. Since surface charge density is inversely proportional to the radius of curvature, the charge density at the sharp tip becomes very high. The electric field near the surface of a conductor is given by E = _0 . Thus, the intense charge density creates a very strong local electric field. This strong electric field ionizes the surrounding air molecules, leading to a continuous corona discharge. This disch

Question 13

What is the upward force acting on a skydiver of mass 60\, kg who is falling at a uniform speed of 2\, m/s ?

Accepted Answer

Since the skydiver is falling at a uniform speed, the acceleration is zero. According to Newton's second law, the net force acting on the skydiver is zero. The upward force (air resistance) must perfectly balance the downward force (weight). F_ up = mg F_ up = 60 9.8 = 588\, N Answer: 588\, N

Question 14

It has been observed that a mirror always forms the image between the pole and the focus, irrespective of the location of the object. Which one of the following is correct in respect of the nature of

Accepted Answer

For a spherical mirror, the mirror formula is given by 1 v + 1 u = 1 f . For a real object placed in front of the mirror, the object distance u is negative. Let u = -x where x > 0. For a convex mirror, the focal length f is positive. Substituting u into the mirror formula gives: 1 v - 1 x = 1 f 1 v = 1 f + 1 x Since both f and x are positive, 1 v > 1 f . This implies that 0 Thus, the image distance v is always positive and less than the focal length f. The image is always formed behind the mirro

Question 15

With respect to electromagnetic waves, the human eye is sensitive to

Accepted Answer

In an electromagnetic wave, the electric field component is responsible for the optical effects. The force exerted by the electric field on the electrons in the retina is much greater than the force exerted by the magnetic field, since the magnetic field amplitude is B = E c and the velocity of electrons is much less than the speed of light c. Due to this, the electric vector is also known as the light vector. Therefore, the human eye is sensitive to the electric field only. Answer: electric fie

Question 16

A glass slab of refractive index 1.5 is cut in the shape of a parallelepiped ABCD as shown in the figure. Surface BC is polished to form a perfect reflector. Light is incident at surface AB from insid

Accepted Answer

For the reflected light to retrace its path, it must strike the polished surface BC normally (perpendicularly). This means the angle between the reflected ray and surface BC must be 90^ . Assuming the given angle /3 (60^ ) is the angle the incident ray makes with the surface AB, by the law of reflection, the reflected ray will also make an angle of 60^ with the surface AB. Consider the triangle formed by the point of incidence on AB, the point of normal incidence on BC, and the vertex B. The sum

Question 17

Three wires each of length L, cross-sectional area A and resistivity are connected as shown in the figure. These are to be replaced by another wire of same resistivity such that the resistance between

Accepted Answer

The resistance of a single wire of length L, cross-sectional area A, and resistivity is given by R = L A . Between points X and Y, there are two such wires connected in parallel. The equivalent resistance R_ XY is: 1 R_ XY = 1 R + 1 R = 2 R R_ XY = R 2 = L 2A Between points Y and Z, there is one such wire. Its resistance is R_ YZ = R = L A . The total resistance between X and Z is the series combination of R_ XY and R_ YZ : R_ XZ = R_ XY + R_ YZ = L 2A + L A = 3 L 2A The new wire has length L_1,

Question 18

The force-time (F - t) graph of a 10\, kg moving object is shown below: What is the final speed of the object?

Accepted Answer

The area under the force-time (F-t) graph gives the impulse, which is equal to the change in momentum of the object. Impulse = Area of the trapezium Area = 1 2 ( sum of parallel sides ) height Area = 1 2 (25 + 15) 20 Area = 1 2 40 20 = 400 \, N s By the impulse-momentum theorem: p = m(v - u) Assuming the object starts from rest (u = 0): 400 = 10 (v - 0) v = 40 \, m/s Answer: 40\, m/s

Question 19

If x is the number of electrons and y is the number of nucleons present in ^ 32 _ 16 S ^ 2- , then which one of the following is correct?

Accepted Answer

The given species is ^ 32 _ 16 S ^ 2- . The atomic number Z of sulfur is 16, which represents the number of protons. Since the species has a charge of -2, it has gained 2 electrons. Therefore, the number of electrons x = 16 + 2 = 18. The mass number A is 32. The number of nucleons is the sum of protons and neutrons, which is equal to the mass number. Therefore, the number of nucleons y = 32. Thus, x = 18 and y = 32.

Question 20

The position vector of a particle is given by r = 3 \,t^2 i + 2 \,t j + 5 \, k . Which one of the following statements is correct?

Accepted Answer

Given position vector r = 3 t^2 i + 2 t j + 5 k Velocity v = d r dt = 2 3 t i + 2 j Instantaneous momentum p = m v = m(2 3 t i + 2 j ) Acceleration a = d v dt = 2 3 i Force F = m a = 2 3 m i Taking the cross product of force and momentum: F p = (2 3 m i ) m(2 3 t i + 2 j ) = 2 6 m^2 k 0 Since the cross product is non-zero, the force is not parallel to the instantaneous momentum. Also, F p = 12m^2t 0, so they are not perpendicular either. Answer: The force acting on the particle is not parallel t

General Science — Previous Year Questions & Solutions