A cockroach is moving with a velocity v in anticlock direction on the rim of a disc of radius R of mass m The moment of inertia of the disc about the axis is II and it is rotating in clockwise direction with an angular velocity ω. If the cockroach stops, the angular velocity of the disc will be

 

A solid body of constant heat capacity 1 J/$$^{\circ}$$C is being heated by keeping it in contact with reservoirs in two ways
(i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat.
(ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat.
In both the cases, body is brought from initial temperature 100$$^{\circ}$$C to final temperature 200$$^{\circ}$$C.
Entropy change of the body in the two cases respectively, is

1) In (2), In 2
2) In 2, 2 ln 2
3) In 2, 2 ln 2
4) In 2,4 In 2

Let the x - z plane be the boundary between two transparent media. Medium 1 in Z ≥ 0  has a refractive index of Ö2  and medium 2 with z < 0 has a refractive index of  Ö3. A ray of light in medium 1 given by the vector    is incident on the plane of separation. The angle of refraction in medium 2 is

1) 45°
2) 60°
3) 75°
4) 30°

The sample of the same gas, x, y and z, for which the ratio of specific heats γ =3/2 have initially the same volume. The volume of the each sample is doubled by adiabatic process in the case of x, by isobaric process in the case of y and by isothermal process in the case of z. If the initial pressure of the sample of x, y and z are in the ratio 2Ö 2 : 1 : 2 then the ratio of the their final pressures is  

1) 2 : 1 : 1
2) 1 : 1 : 1
3) 1 : 2 : 1
4) 1 : 1 : 2 

A charge q is placed at the mid-point of the line joining two equal charges each of Q. If the whole system is in equilibrium, then the value of q is    

Energy required for the electron excitation in Li from the first to the third Bohr orbit is

1) 36.3 eV
2) 108.8 eV
3) 122.4 eV
4) 12.1 eV

An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by  where v is the instantaneous speed. The time taken by the object, to come to rest, would be

1) 1 s 2) 2 s  3)  4 s  4)  8s

A particle moves along positive branch of the curve y=x/ 2 where x=t3/ 3, x  and y are measured in metres and t in seconds, then

1) The acceleration of particle at t=2s is iˆ+2jˆ
2) The acceleration of particle at t=1s is 2iˆ+ jˆ
3) The velocity of particle at t=2s is iˆ+1/2 jˆ
4) The velocity of particle at t=1s is 1/2 iˆ+ jˆ 

The resultant of three vectors 

1) r
2) 2r
3) r(1 + Ö 2)
4) r(Ö 2 - 1)

Two blocks of masses 10 kg an 4 kg are connected by a spring of negligible mass and placedon a frictionless horizontal surface. An impulse gives velocity of 14 m/s to the heavier block inthe direction of the lighter block. The velocity of the centre of mass is

1) 30 m/s   2) 20 m/s  3) 10 m/s   4) 5 m/s