sunday

In a situation, a board is moving with a velocity v with respect to earth, while a man A and man B are running with a velocity 2v with respect to earth and both men are running from the opposite ends of the board at the same time, as shown. Length of the board is L. If they meet after time T, then

• value of T is L/4v

• value of T is L/2v

• Displacement of man B with respect to board in time T is 3L/4

• Displacement of man A with respect to board in time T is L/4

An object is moving in the xy plane with the position vector is given by and velocity vector is . Consider a point O at origin .Distance of object from origin in decreasing, if

• v > 0, v < 0 & x < 0, y > 0

• v < 0, v > 0 & x > 0, y < 0

• xv + yv < 0

• – xv + yv < 0

Two refracting media are separated by a spherical interface as shown in the figure. PP′ is the principal axis, μ and μ are the refractive indices of medium of incidence and medium of refraction respectively. Then:

• if μ > μ, then there cannot be a real image of real object

• if μ > μ, then there cannot be a real image of virtual object

• if μ > μ, then there cannot be a virtual image of virtual object

• if μ > μ, then there cannot be a real image of real object

In the figure shown radius of curvature of either surface of equi convex half lens is 40 cm and refractive index 1.5. Its one side is silvered. A plane mirror is also placed. A small object O is placed such that there is no parallax between final image formed by lens and mirror. If transverse length of final image formed by lens system is twice that formed by mirror. Choose the correct options :

• a = 2.5 cm

• b = 5 cm

• Distance of image from object is 15 cm

• Image formed by lens system is virtual

A bead of mass m is kept at a distance a from the axis of rotation of a smooth massless tube. The tube is rotated on a smooth horizontal surface along a vertical axis perpendicular to the length L of the tube and passing through one of its end 'O' with constant angular velocity ω.

• The speed of the bead relative to tube when it is at distance r from axis of rotation is ω

• The speed of the bead relative to tube when it is at distance r from axis of rotation is ω

• The work done by the centrifugal force in the frame of the tube when the bead reaches at distance r from the axis starting from radius a is mω(r – a)

• The work done by the centrifugal force in the frame of the tube when the bead reaches at distance r from the axis starting from radius a is mω (r – a)

A car is accelerating on a horizontal road with acceleration = 20 m/s. A box that is placed inside the car, of mass m = 10 kg is put in contact with the vertical wall as shown. The friction coefficient between the box and the wall is μ = 0.6.

• The acceleration (with respect to ground) of the box will be 20 m/sec

• The friction force acting on the box will be 100 N

• The contact force between the vertical wall and the box will be 100N

• The net contact force between the vertical wall and the box is only of electromagnetic in nature.

A car is travelling in steady rain with constant acceleration in a straight line. When it begins to move the driver sees that the raindrops make an angle of 37° with the vertical. After 20 s, the driver observes that the raindrops make an angle of 53° with vertical in same direction. The acceleration of the car is x cm/s. Find the value of 2x. Rain is falling at 3 m/s relative to the ground.

A river is flowing with velocity 5 km/hr relative to the ground as shown in the figure. A boat starts from A and reaches the other bank by covering shortest possible distance. Velocity of boat in still water is 3 km/hr. The distance (in m) boat covers is s. The value of is

Two inclined planes OA and OB of inclinations to the horizontal α and β, each equal to 30° are placed as shown in the figure. A particle is projected at an angle of 90° with plane OA from point A and its strikes the plane OB at point B normally. If the speed of projection in m/s is x. Fill the value of 8x. (given that OA = OB = 20 cm and g = 10 m/s)

The backside of a truck is open and a box of 40 kg is placed 5 m away from the rear end. The coefficient of friction of the box with the surface of the truck is 0.15. The truck starts from rest with acceleration 2 m s. Calculate the distance (in m) covered by the truck when the box falls off.