1 The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1% , the maximum error in determining the density is A) 3.5% B) 4.5% C) 2.5% D) 6%
2 A particle is moving in a circular path of radius a under the action of an attractive potential $U=-\frac{k}{2r^{2}}$ , Its total energy is A) $-\frac{k}{4a^{2}}$ B) 0 C) $\frac{K}{2a^{2}}$ D) $-\frac{3k}{2a^{2}}$
3 A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the n th power of R. If the period of rotation of the particle is T, then A) $T\propto R^{\frac{3}{2}}$ For any n B) $T\propto R^{\frac{n}{2}}$ C) $T\propto R^{\frac{n}{2}+1}$ D) $T\propto R^{\frac{(n+1)}{2}}$
4 From a unifrom circular disc of radius R and mass 9 M, a small disc of radius $\frac{R}{3}$ is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is A) $4MR^{2}$ B) $10MR^{2}$ C) $\frac{40}{9}MR^{2}$ D) $\frac{37}{9}MR^{2}$
5 In the figure below , the switches S1 and S2 are closed simultaneously at t=0 and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current I in the middle wires reaches its maximum magnitude Imax at time $t=\tau$ . which of the following statements is (are) true ? A) $I_{max}=\frac{V}{2R}$ B) $I_{max}=\frac{V}{4R}$ C) $\tau =\frac{L}{R} In 2$ D) $\tau =\frac{2L}{R} In 2$
6 A ring and a disc are initially at rest , side by side , at the top of an inclined plane which makes an angle 60° with the horizontal . They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is $\frac{(2-\sqrt{3})}{\sqrt{10}}$ s, then the height of the top of the inclined plane, in meters is ... [Take, g=10 m s-2 ] A) 0.50 m B) 0.95m C) 0.75m D) 1.00m
7 The relation between $[\epsilon_{0}]$ and $[\mu_{0}]$ A) $[\mu_{0}]= [\epsilon_{0}][L]^{2}[T]^{-2}$ B) $[\mu_{0}]= [\epsilon_{0}][L]^{-2}[T]^{2}$ C) $[\mu_{0}]= [\epsilon_{0}^{}]^{-1}[L]^{2}[T]^{-2}$ D) $[\mu_{0}]= [\epsilon_{0}^{}]^{-1}[L]^{-2}[T]^{2}$
8 A particle of mass m is initially at rest at the origin . It is subjected to a force and starts moving along the X-axis . Its kinectic energy K changes with time as $\frac{\text{d}K}{\text{d}t}=\gamma t$ , where $\gamma $ is a positive constant of appropriate dimensions. Which of the following statements is (are) true? A) The force applied on the particle is constant B) The speed of the particle is proportional to time C) The distance of the particle from the origin increases linearly with time. D) The force is conservative.
9 In a radioactive decay chain, $_{90}^{232}Th$ nucleus decays to $_{82}^{212}Pb$ nucleus. Let $N_{\alpha}$ and $N_{\beta}$ be the number of $\alpha$ and $\beta$- particles repectively, emitted in this decay process. Which of the following statements is(are) true? A) $N_{\alpha}=5$ B) $N_{\alpha}=6$ C) $N_{\beta}=2$ D) $N_{\beta}=4$
10 A particle of mass 10-3 kg and charge 1.0 C is initially at rest. At time t=0, the particle comes under the influence of an electric field E (t)= E0 sin ωt $\hat{i}$, where E0 = 1.0N C-1 and ω=103 rad s-1 . Consider the effect of only the electrical force on the particle . Then , the maximum speed in ms-1 , attained by the particle at subsequent times is.......... A) 1 B) 2 C) 1.5 D) 3
11 A steel wire of diameter 0.5 mm and Young's modulus 2 × 1011 N m-2 carries a load of mass m. The length of the wire with the load is 1.0 m. A vernier scale with 10 divisions is attached to the end of this wire. Next to the steel wire is reference wire to which a main scale, of least count 1.0 mm , is attached. The 10 divisions of the vernier scale correspond to 9 divisions of the main scale. Initially , the zero of vernier scale coincides with the zero of main scale . If the load on the steel wire is increased by 1.2 kg, the vernier scale division which concides with a main scale division is ........... Take , g= 10 m s-1 and π =3.2) A) 3rd Division B) 5th Division C) 6th Division D) 9th Division
12 One mole of monoatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is 100K and the universal gas constant R= 8.0 j mol-1 K-1 , the decrease in its internal energy in joule, is .............. A) 450 J B) 900 J C) 850 J D) 750 J
13 In a photoelectric experiment , a parallel beam of monochromatic light with power of 200 W is incident on a perfectly absorbing cathode of work function 6.25 eV . The frequency of light is just above the threshold frequency, so that the photoelectrons are emitted with negligible kinetic energy. Assume that the photoelectron emission efficiency is 100% . A potential difference of 500 V is applied between the cathode and the anode. All the emitted electrons are incident normally on the anode and are absorbed. The anode experiences a force F= n × 10-4 N due to the impact of the eletrons. The value of n is .................(Take mass of the electron, me =9× 10-31 kg and eV = 1.6 × 10-19 J) A) 26 B) 24 C) 42 D) 12
14 Consider a hydrogen -like ionised atom with atomic number Z , with a single electron. In the emission spectrum of atom, the photon emitted in the n= 2 to n=1 transition has energy 74.8 eV higher than the photon emitted in the n=3 to n=2 transition.The ionisation energy of the hydrogen atom is 13.6 eV. The value of Z is.......... A) 3 B) 6 C) 4 D) 2
15 One mole of a monoatomic ideal gas undergoes four thermodynamic processes as shown schematically in the pV - diagram below. Among these four processes, one is isobaric, one is isochoric , one is isothermal and one is adiabatic. Match the processes mentioned in List -I with the corresponding statements in List -II A) $P\rightarrow4;Q\rightarrow3;R\rightarrow1;S\rightarrow2$ B) $P\rightarrow1;Q\rightarrow3;R\rightarrow2;S\rightarrow4$ C) $P\rightarrow3;Q\rightarrow4;R\rightarrow1;S\rightarrow2$ D) $P\rightarrow3;Q\rightarrow4;R\rightarrow2;S\rightarrow1$