At what height from the surface of earth the gravitation potential and the value of g are -5.4 x 10⁷ J kg^-2 and 6.0 m/s² respectively? (Take the radius of the earth as 6400 km)

• 1600 km

• 1400 km

• 2000 km

• 2600 km

A car is negotiating a curved road of radius R. The road is banked at angle θ. The coefficient of friction between the tyres of the car and the road is μ_s . The maximum safe velocity on this road is,

A body of mass 1 kg begins to move under the action of a time dependent force F =  N, where  are units vectors along X and Y axis. What power will be developed by the force at the time (t)?

• (2t² + 4t⁴) W

• (2t³ + 3 t⁴) W

• (2t³ + 3t⁵) W

• (2t + 3t³)W

From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc, about a perpendicular axis, passing through the centre?

• 13 MR²/32

• 11MR²/32

• 9MR²/32

• 15MR²/32

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is,

• 90^o

• 45^o

• 180^o

• 0^o

If the velocity of a particle is v = At + Bt², where A and B are constants, then the distance travelled by it between 1 s and 2 s is,

• 3A + 7B

• 

• 

• 

A disc and a sphere of the same radius but differnt masses roll off two inclined planes of the same altitude and length. which one of the two objects gets to the bottom of the plane first?

• Sphere

• Both reach at the same time

• Depends on their masses

• Disc

Two identical charged spheres suspended from a  common point by two massless strings of lengths l, are initially at a distance d (d < l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then, v varies as a function of the distance x between the sphere, as

• vx

• 

• vx^-1

• 

A particle  moves so that its position vector is given by r = cos  where  is a constant. Which of the following is true?

• velocity and acceleration both are parallel to r

• velocity is perpendicular to r and acceleration is directed towards the origin

• velocity is perpendicular to r and acceleration is directed away from the origin

• velocity and acceleration both are perpendicular to r

A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected  to a torque which produces a constant angular acceleration of 2.0 rad/sec². It's net acceleration in m/s² at the end of 2.0 s is a approximately.

• 7.0

• 6.0

• 3.0

• 8.0