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 the horizontal surface is 0.15. The minimum weight m that should be put on top of m₂ to stop the motion is :

• 10.3 kg

• 18.3 kg

• 27.3 kg

• 43.3 kg

2.

In a collinear collision, a particle with an initial speed v0 strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after the collision, is:

• 

• v_o/4

• 

• v₀/2

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:

• $T\propto R^{n/2}$

• $T\propto R^{3/2} for any n$

• $T\propto R^{\frac{n}{2}+1}$

• $T\propto R^{\frac{n+1}{2}}$

It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is p_d; while for its similar collision with carbon nucleus at rest, fractional loss of energy is p_c. The values of p_d and p_c are respectively :

• (0,1)

• (.89,.28)

• (.28,.89)

• (0,0)

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 10¹²/sec. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 and Avagadro number = 6.02 × 10²³ gm mole^–1)

• 5.5 N/m

• 6.4 N/m

• 7.1 N/m

• 2.2 N/m

A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 x 10³ kg/m³ and its Young’s modulus is 9.27 x 10¹⁰ Pa. What will be the fundamental frequency of the longitudinal vibrations?

• 7.5 kHz

• 5 kHz

• 2.5 kHz

• 10 kHz

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:

• 6%

• 2.5%

• 3.5%

• 4.5%

Two moles of an ideal monoatomic gas occupies a volume V at 27°C. The gas expands adiabatically to a volume 2 V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.

• (a) 195 K (b) 2.7 kJ

• (a) 189 K (b) 2.7 kJ

• (a) 195 K (b) –2.7 kJ

• (a) 189 K (b) – 2.7 kJ

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 the area a floats on the surface of the liquid, covering an 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, (dr/r), is

• mg/Ka

• Ka/mg

• Ka/3mg

• mg/3Ka