1 A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container.When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere $\frac{dr}{r}$ is A) $\frac{Ka}{mg}$ B) $\frac{Ka}{3mg}$ C) $\frac{mg}{3Ka}$ D) $\frac{mg}{Ka}$
2 Two masses m1= 5 kg and m2 = 10 kg connected by an inextensible string over a frictionless pulley , are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of m2 to stop the motion is A) 18.3 kg B) 10.3 kg C) 43.3 kg D) 27.3 kg
3 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%
4 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) $-\frac{3k}{2a^{2}}$
5 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) $T\propto R^{\frac{(n+1)}{2}}$
6 A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross- section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, ($\frac{\text{d}r}{\text{}r}$) is A) $\frac{Ka}{mg}$ B) $\frac{Ka}{3mg}$ C) $\frac{mg}{3Ka}$ D) $\frac{mg}{Ka}$
7 Two moles of an ideal monoatomic gas occupies a volume V at 27° C. The gas expands adiabatically to a Volume 2 V. Calculate(i) the final temperature of the gas and (ii) change in its internal energy. A) (i)189 K (ii) 2.7 KJ B) (i) 195 K (ii) -2.7 KJ C) (i) 189 K (ii) -2.7 KJ D) (i) 195 K (ii) 2.7 KJ
8 The reading of the ammeter for a silicon diode in the given circuit is A) 0 B) 15mA C) 11.5mA D) 13.5mA
9 On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10cm. The resistance of their series combination is 1kΩ. How much was the resistance on the left slot before interchanging the resistances? A) 990Ω B) 505Ω C) 550Ω D) 910Ω
10 Two men are walking along a horizontal straight line in the same direction.The man in front walks at speed 1.0 ms-1 and the man behind walks at a speed 2.0 ms-1 . A third man is standing at a height 12 m above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency 1430Hz. The speed of sound in air 330 ms-1. At the instant , when the moving men are 10 m apart, the stationary man is equidistant from them. The frequency of beats in Hz, heard by the stationary man at this instant, is.... A) 3 Hz B) 5 Hz C) 7 Hz D) 6 Hz
11 A spring block system is resting on a frictionless floor as shown in the figure. The spring constant is 2.0 Nm-1 and the mass of the block is 2.0 kg. Ignore the mass of the spring. Initially ,the spring is in an unstretched condition. Another block of mass 1.0kg moving with a speed of 2.0 ms-1 collides elastically with the first block. The collision is such that the 2.0kg block does not hit the wall. The distance , in metres, between the two blocks when the spring returns to its unstretched position for the first time after the collision is... A) 2.09m B) 2.5m C) 3.0m D) 1.6 m
12 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.
13 A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass m= 0.4 kg is at rest on this surface . An impulse of 1.0 N s is applied to the block at time t=0, so that it starts moving along the x- axis with a velocity $v_{t}=v_{0}e^{\frac{-t}{\tau}}$ where v0 is a constant and $\tau=4$ s. The displacement of the block, in metres at $t=\tau$ is............... ( Take , e-1 =0.37) A) 6.30 B) 6.75 C) 5.60 D) 5.36
14 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
15 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
