Problem 1
Gravitational collapse is the contraction of an astronomical object under its own gravity. This draws the matter inwards towards the centre of gravity. A neutron star is an example of the collapsed core of a giant star. A certain neutron star of radius 10 km is of mass \(1.5 M_{\odot}\). The acceleration due to gravity on the surface of the neutron star is nearly
(a) \(2.0 \times 10^8 \mathrm{~m} / \mathrm{s}^2\)
(b) \(2.0 \times 10^{12} \mathrm{~m} / \mathrm{s}^2\)
(c) \(2.6 \times 10^{16} \mathrm{~m} / \mathrm{s}^2\)
(d) \(2.6 \times 10^{20} \mathrm{~m} / \mathrm{s}^2\)
Problem 2
The tympanic membrane (ear drum) is a very delicate component of the human ear. Typically, its diameter is 1 cm . The maximum force the ear can withstand is 2.5 N . In case a diver has to enter sea water of density \(1.05 \times 10^3 \mathrm{~kg} / \mathrm{m}^3\) without any protective gear, the maximum safe depth for the diver to go into water is about
(a) 12 m
(b) 9 m
(c) 3 m
(d) 1.5 m
Problem 3
Two illuminated point objects \(\mathrm{O}_1\) and \(\mathrm{O}_2\) are placed at a distance 24 cm from each other along the principal axis of a thin convex lens of focal length 9 cm such that images of both the objects are formed at the same position. Then the respective distances of the lens from \(\mathrm{O}_1\) and \(\mathrm{O}_2\) (in cm ) are
(a) 12 and 12
(b) 18 and 6
(c) 14 and 10
(d) 16 and 8
Problem 4
A nuclear reactor is working at \(30 \%\) efficiency (i.e. conversion of nuclear energy to electrical energy). In this reactor \({ }_{92}^{235} \mathrm{U}\) nucleus undergoes fission and releases 200 MeV energy per atom. If 1000 kW of electrical power is obtained in this reactor, then the number of atoms disintegrated (undergone fission) per second in the reactor is
(a) \(1.04 \times 10^{17}\)
(b) \(6.5 \times 10^{12}\)
(c) \(3.125 \times 10^{12}\)
(d) \(3.25 \times 10^{32}\)
Problem 5
Two blocks A and B are in contact with each other and are placed on a frictionless horizontal surface. A force of 90 N is applied horizontally on block A (situation I) and the same force is applied horizontally on block B (situation II). Mass of A is 20 kg and B is 10 kg . Then the correct statement is
(a) Since both the blocks are in contact, magnitude of force by block A on B will be 90 N (situation I) and magnitude of force by block B on A will also be 90 N (situation II).
(b) Magnitude of force by block A on B is 30 N (situation I ) and magnitude of force by block B on A is 60 N (situation II).
(c) Magnitude of force by block A on B is 60 N (situation I ) and magnitude of force by block B on A is 30 N (situation II).
(d) The 90 N force will produce acceleration of different magnitudes in A and B .
Problem 6
In the adjoining circuit, \(R=5 \Omega\). It is desired that the voltage across \(R_x\) should be 6 V , then the value of \(R_x\) should be
(a) \(4 \Omega\)
(b) \(12 \Omega\)
(c) \(16 \Omega\)
(d) \(20 \Omega\)
Problem 7
An infinitely long conductor when carrying current (I), produces a magnetic field (B) around it. If such a conductor is placed along the X-axis, then the magnitude of (B) at a distance (r) is given by the relation \(B=\frac{\mu_0}{4 \pi} \frac{2 I}{r}\), (where \(\frac{\mu_0}{4 \pi}=10^{-7} \mathrm{NA}^{-2}\) is a constant). The following figure shows such an infinitely long conductor placed along X -axis carrying current (I) and (B) at (S) is \(2 \times 10^{-4} \mathrm{~T}\), directed into the plane of the paper at S. Given \(r=1 \mathrm{~cm}\). Then, the correct statements are
(a) \(I=10 \mathrm{~A}\)
(b) The number of electrons transported across the cross section of the conductor during time 1 s is \(6.25 \times 10^{19}\)
(c) The direction of current (I) is from \(X_2\) to \(X_1\).
(d) The electrons will flow in the direction \(\mathrm{X}_2\) to \(\mathrm{X}_1\).
Problem 8
The ratio of the charge of an ion or subatomic particle to its mass \((q / m)\) is called specific charge. Then the correct options are
(a) SI unit of specific charge can be written as \(\mathrm{A} \cdot \mathrm{s} / \mathrm{kg}\).
(b) If all the isotopes of hydrogen are ionized then tritium will have least specific charge among them.
(c) specific charge of an \(\alpha\)-particle will be greater than that of an electron.
(d) specific charge ratio of an electron is \(1.75 \times 10^{11} \mathrm{C} / \mathrm{kg}\).
Problem 9
A girl (G) walks into a room along the path shown by the dashed line (see figure on right). She tries to observe images of small toys numbered 1,2 , and 3 in the plane mirror on the wall. The order in which she will see images of the toys is:
(A) 3,2,1
(B) 3,2
(C) 1, 2, 3
(D) 2, 3
Problem 10
A heating element in the form of a wire with uniform circular cross sectional area has a resistance of \(310 \Omega\), and can bear a maximum current of 5.0 A . The wire can be cut into pieces of equal length. The number of pieces, arranged suitably, so as to draw maximum power when connected to a constant voltage of 220 V , is
(A) 7
(B) 8
(C) 44
(D) 62
Problem 11
Consider the following two statements
Statement \(S_1\): If you put 100 g ice at \(0^{\circ} \mathrm{C}\) and 100 g water at \(0^{\circ} \mathrm{C}\) into a freezer, which is maintained at \(-10^{\circ} \mathrm{C}\), the ice will eventually lose the lager amount of heat.
Statement \(S_2\) : At \(0^{\circ} \mathrm{C}\), water is denser than ice
Choose the correct statement among the following.
(A) Both \(S_1\)and \(S_2\) are true and \(S_2\) is the correct explanation of \(S_1\)
(B) Both \(S_1\) and \(S_2\) are true and \(S_2\) is not the correct explanation of \(S_1\)
(C) \(S_1\) is true but \(S_2\) is false
(D) \(S_1\) is false but \(S_2\) is true
Problem 12
Consider the paths of (1) Halley's Comet near the sun, and (2) an alpha particle scattered by a nucleus. In the figures below, the dots represent the Sun/Nuclei, and the curves with arrows mark the paths of the comet/alpha particle schematically.The correct statement about the trajectories is
(A) I represents trajectory for Halley's Comet and II for the scattering of alpha particles.
(B) III represents trajectory for Halley's Comet and II for the scattering of alpha particles
(C) II represents trajectory for Halley's Comet and I for scattering of alpha particles
(D) II represents trajectory for Halley's Comet and III for scattering for scattering of alpha particles.
