Two identical piano wires kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beats/s when both the wires oscillate together would be

• 0.02

• 0.03

• 0.04

• 0.04

2.

A coil has resistance 30 O and inductive reactance 20 O at 50 Hz frequency. If an AC source 200 V, 100 Hz, is connected across the coil, the current in the coil will be

• 4.0 A

• 8.0 A

• 
• 

A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are, respectively, M and R.G are gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth is 

The density of material in CGS system of units is 4g/ cm².In a system of units in which unit of lengths is 10 cm and unit of mass is 100 g, the value of density of material will be 

• 0.4

• 40

• 400

• 400

A particle covers half of its total distance with speed v₁ and the rest half distance with speed v₂. Its average speed during the complete journey is

• v₁v₂ / v₁ + v₂

• 2v₁v₂/v₁ + v₂

• 2v₁²v²₂ / v₁² + v²₂

• 2v₁²v²₂ / v₁² + v²₂

A conveyor belt is moving at a constant speed of 2 m/s. A box is gently dropped on it. The coefficient of friction between them is μ = 0.5. The distance that the box - will move relative to belt before coming to rest on it taking 

g= 10 ms^{-2 is}

• 1.2 m

• 0.6 m

• zero

• zero

A mass m moving horizontally (along the x -axis) with velocity v collides and sticks to mass of 3m moving vertically upward (along the y -axis) with velocity 2v. The final velocity of the combination

A small mass attached to a string rotats on frictionless table top as shown. If the tension is the string is increased by pulling the string causing the radius of the circular  motion to decrease by a factor of 2, the kinetic energy of the mass will

• remain constant

• increase by a factor of 2

• increase by a factor 4 

• increase by a factor 4 

A particle of mass M is situated at the centre of spherical shell of mass and radius a. Th magnitude of the gravitational potential at a points situated at a/2 distance from the centre, will be

• 2GM/a

• 3GM/a

• 4GM/a

• 4GM/a

A projectile is fired an angle of 45^o with the horizontal.Elevation angle of the projectile at the highest point as seen from the point of projection is 

• 60^o

• tan^-1(1/2)

• 
•