Problem 1
Two blocks A and B of masses 1 kg and 4 kg respectively are moving with equal kinetic energies. Read the following statements \(S_1\) and \(S_2\)
Statement \(S_1\) : Ratio of speed of the block A to that of B is (1: 2)
Statement \(S_2\) : Ratio of magnitude of linear momentum of (A) to that of (B) is (1: 2)
Now choose the correct option:
(a) Both \(\mathrm{S}_1\) and \(\mathrm{S}_2\) are true
(b) Both \(\mathrm{S}_1\) and \(\mathrm{S}_2\) are false
(c) \(S_1\) is true, \(S_2\) is false
(d) \(\mathrm{S}_1\) is false, \(\mathrm{S}_2\) is true
Problem 2
The mass of a straight copper wire is 20.95 g and its electrical resistance is \(0.065 \Omega\). If the density and resistivity of copper are \(\mathrm{d}=8900 \mathrm{~kg} / \mathrm{m}^3\) and \(\rho=1.7 \times 10^{-8}\) ohm-meter respectively, the length of the copper wire is
(a) 3 m
(b) 6 m
(c) 12 m
(d) date is insufficient
Problem 3
It is known that the speed of sound in a gas is directly proportional to square root of its absolute temperature T measured in Kelvin i.e. \(v \propto \sqrt{T}\) Speed of sound in air at \(0^{\circ} \mathrm{C}\) is \(332 \mathrm{~m} / \mathrm{s}\). On a hot day, the speed of sound was measured \(360 \mathrm{~m} / \mathrm{s}\) in NCR Delhi, the temperature of air in Delhi on that very day must have been close to
(a) \(40^{\circ} \mathrm{C}\)
(b) \(42^{\circ} \mathrm{C}\)
(c) \(44^{\circ} \mathrm{C}\)
(d) \(48^{\circ} \mathrm{C}\)
Problem 4
A small bar magnet is allowed to fall vertically through a metal ring lying in a horizontal plane. During its fall, the acceleration of the magnet in the region close to the ring must be ( g is the acceleration due to gravity)
(a) equal to (g)
(b) less than (g) and uniform
(c) less than g and non-uniform
(d) greater than (g) and uniform
Problem 5
A U-tube of uniform cross section contains two different liquids in its limbs namely water (density \(1.0 \times 10^3 \mathrm{~kg} / \mathrm{m}^3) \) and Mercury (density \(13.6 \times 10^3 \mathrm{~kg} / \mathrm{m}^3) \) as shown in figure. The difference of height of mercury column in two limbs of the tube is \(\mathrm{H}=1.5 \mathrm{~cm}\). The height h of the water column in the left limb above the Mercury column must be nearly (Neglect surface tension effects)
(a) 13.6 cm
(b) 20.4 cm
(c) 27.0 cm
(d) 9.0 cm
Problem 6
An object pin is placed at a distance 10 cm from first focus of a thin convex lens on its principal axis, the lens forms a real and inverted image of this object pin at a distance 40 cm beyond the second focus. The focal length of the lens is
(a) 16 cm
(b) 20 cm
(c) 25 cm
(d) 40 cm
Problem 7
A bullet of mass 0.25 kg moving horizontally with velocity \(v(\mathrm{~m} / \mathrm{s})\) strikes a stationary block of mass 1.00 kg suspended by a long inextensible string of negligible mass and length \(\ell\). The bullet gets embedded in the block and the system rises up to maximum height \(\mathrm{h}=19.6 \mathrm{~cm}\) (as shown in the figure. The string still remains taut). The value of initial speed (v) of the bullet is
(a) \(5.9 \mathrm{~m} / \mathrm{s}\)
(b) \(7.8 \mathrm{~m} / \mathrm{s}\)
(c) \(9.8 \mathrm{~m} / \mathrm{s}\)
(d) \(11.8 \mathrm{~m} / \mathrm{s}\)
Problem 8
The equivalent resistance between points A and B in the following electrical network is
(a) \(\frac{3}{4} \Omega\)
(b) \(\frac{4}{3} \Omega\)
(c) \(\frac{2}{5} \Omega\)
(d) \(\frac{9}{14} \Omega\)
Problem 9
The order of magnitude of the pressure (in pascal) exerted by an adult human on the Earth when he stands bare footed on the Earth on both of his legs, is
(a) \(10^2\)
(b) \(10^4\)
(c) \(10^7\)
(d) \(10^9\)
Problem 10
On the board of an experiment, three bulbs \(\mathrm{B}_1(100 \mathrm{~W}, 200 \mathrm{~V})\), \(\mathrm{B}_2(60 \mathrm{~W}, 200 \mathrm{~V})\) and \(\mathrm{B}_3(40 \mathrm{~W}, 200 \mathrm{~V})\) are connected to a 200 V fluctuating supply with a fuse in series as shown in the figure. The electric current rating of the fuse required in the circuit to protect all the three bulbs must be
(a) 0.2 Amp
(b) 0.3 Amp
(c) 0.5 Amp
(d) 1.0 Amp
Problem 11
An ant is sitting on the principal axis of a convex mirror of focal length (f), at a distance (2 f) from the pole in front of the mirror. It starts moving on principal axis towards the mirror. During the course of motion, the distance between the ant and its image
(a) throughout increases
(b) throughout decreases
(c) first increases, then decreases
(d) first decreases, then increases
Problem 12
You are given three resistance of values \(2 \Omega, 4 \Omega\) and \(6 \Omega\). Which of the following values of equivalent resistance is not possible to get by using/arranging these three resistors in any circuit?
(a) Less than \(2 \Omega\)
(b) Equal to \(4.4 \Omega\)
(c) Equal to \(5.5 \Omega\)
(d) Equal to \(7.6 \Omega\)
Problem 13
ABC is a 0.8 meter long curved wire track in a vertical plane. A bead of mass 3 g is released from rest at A . It slides along the wire and comes to rest at C . The average frictional force opposing the motion in a single trip from A to C is
(a) \(18.40 \times 10^{-3} \mathrm{~N}\)
(b) \(29.4 \times 10^{-3} \mathrm{~N}\)
(c) \(11.04 \times 10^{-3} \mathrm{~N}\)
(d) \(7.36 \times 10^{-3} \mathrm{~N}\)
Problem 14
Two long straight conductors 1 and 2 , carrying parallel currents \(I_1\) and \(I_2\) in the same direction, are lying parallel and close to each other, as shown in the figure. \(F_e\) and \(F_m\) respectively represent the electric and the magnetic forces, applied by conductor 1 on conductor 2. Choose the correct alternative regarding nature of \(\mathrm{F_e}\) and \(\mathrm{F_m}\)
(a) \(\mathrm{F_e}\) is repulsive while \(\mathrm{F_m}\) is attractive
(b) \(\mathrm{F_e}\) is repulsive and \(\mathrm{F_m}\) is repulsive too
(c) \(F_e\) is zero and \(F_m\) is repulsive
(d) \(\mathrm{F_e}\) is zero and \(\mathrm{F_m}\) is attractive
Problem 15
A doctor measures the temperature of a patient by a digital thermometer as \(37.3^{\circ} \mathrm{C}\). As a Physics student you will record his temperature in Kelvin as
(a) 310.30 K
(b) 310.45 K
(c) 310.46 K
(d) 310.31 K
Problem 16
Two planets \(P_1\) and \(P_2\) are moving around the Sun, in circular orbits of radii \(10^{13} \mathrm{~m}\) and \(10^{12} \mathrm{~m}\) respectively. The ratio of the orbital speeds of planets \(P_1\) and \(P_2\) in their respective orbits is
(a) \(\sqrt{10}\)
(b) 10
(c) \(10 \sqrt{10}\)
(d) \(\frac{1}{\sqrt{10}}\)
Problem 17
Crane A and crane B take 1 minute and 2 minute respectively to lift a car of mass 2 ton ( 2000 kg ) upward through a vertical height \(\mathrm{h}=3\) meter. If the efficiencies of the engines (defined as the ratio of work output to fuel energy input) of both the cranes are equal, your inference is that
(a) the power supplied by crane B is 1000 kW
(b) the crane A and the crane B consume equal amount of fuel
(c) the power supplied by crane A is more than the power supplied by crane B
(d) the crane A consumes more fuel in lifting the car than the crane B
Problem 18
Two tungsten filament bulbs with rating 100 watt, 200 volt and 60 watt, 200 volt are connected in series with a variable supply of \(0-400 \mathrm{~V}\) range, as shown. The supply voltage is gradually increased from 0 to 400 V . Choose the correct statement(s).
(a) When supply voltage is 200 volt, 60 W bulb glows brighter
(b) When supply voltage is 200 volt, total power dissipated in both the bulbs is greater than 37.5 W
(c) When the supply voltage is 400 V , the 100 W bulb gets fused
(d) When supply voltage becomes 400 V , none of the bulbs glow
Problem 19
A solid sphere of radius \(R=10 \mathrm{~cm}\) floats in water with \(60 \%\) of its volume submerged. In an oil, this sphere floats with \(80 \%\) of its volume submerged. If the density of water is \(1000 \mathrm{~kg} / \mathrm{m}^3\). The correct statement(s) is/are that
(a) the density of the material of sphere is \(600 \mathrm{~kg} / \mathrm{m}^3\)
(b) the density of the oil is \(750 \mathrm{~kg} / \mathrm{m}^3\)
(c) the weight of the sphere in air is close to 24.64 N
(d) the loss in weight of the sphere when floating in oil is close to 30.82 N
Problem 20
A particle starts moving from origin O along (x) axis. The velocity-time graph of motion of particle is given below. The positive values of (v) refer to direction of motion along (+x) axis, the negative values of (v) refer to direction of motion along (-x) direction. Choose the correct statement(s).
(a) Initial acceleration of the particle is \(4 \mathrm{~m} / \mathrm{s}^2\)
(b) The displacement of particle from origin is 130 m after 16 second
(c) Average speed of the moving particle during (0-16) second is \(11.88 \mathrm{~m} / \mathrm{s}\)
(d) Somewhere during the motion for (0-16) second, the retardation of the particle is \(10 \mathrm{~m} / \mathrm{s}^2\)
