The angle subtended by the vector $\mathrm{A} = 4\stackrel{\wedge }{\mathrm{i}} + 3\stackrel{\wedge }{\mathrm{j}} + 12\stackrel{\wedge }{\mathrm{k}}$ with the x-axis

• ${\sin }^{-1}\left(\frac{3}{13}\right)$

• ${\sin }^{-1}\left(\frac{4}{13}\right)$

• ${\cos }^{-1}\left(\frac{4}{13}\right)$

• ${\cos }^{-1}\left(\frac{3}{13}\right)$

The velocity of a particle v at an instant t is given by v = at + bt²  the dimension of b is 

• [L]

• [LT^-1]

• [LT^-2]

• [LT^-3]

The distance travelled by an object along a straight line in time t is given by s= 3 − 4t + 5t², the initial velocity of the object is

• 3 unit

• − 3 unit 

• 4 unit

• − 4 unit

A pellet of mass 1 g is moving with an angular velocity of 1 rad/s along a circle of radius 1 m the centrifugal force is

• 0.1 dyne

• 1 dyne

• 10 dyne

• 100 dyne

Two point objects of masses 1.5 g and 2.5 g respectively area at a distance of 16 cm apart, the centre of gravity is at a distance x from the object of mass 1.5 g where x is

• 10 cm

• 6 cm

• 13 cm

• 3 cm

6.

If the earth shrinks such that its mass does not change but radius decreases to one quarter of its original value then one complete day will take

• 96 h

• 48 h

• 6 h

• 1.5 h

A shell of mass 10 kg is moving with a velocity of 10 ms^-1 when it blasts and forms two parts of mass 9 kg and 1 kg respectively. If the 1^st mass is stationary, the velocity of the 2^nd is

• 1 m/s

• 10 m/s

• 100 m/s

• 1000 m/s

Force required to move a mass of 1 kg at rest on a horizontal rough plane (µ = 0.1 and g =9.8 ms^-2) is 

• 0.98 N

• 0.49 N

• 9.8 N

• 4.9 N

A rocket of mass 100 kg burns 0.1 kg of fuel per sec. If velocity of exhaust gas is 1 km/sec, then it lifts with an acceleration of

• 1000 ms^-2

• 100 ms^-2

• 10 ms^-2

• 1 ms^-2

The weight of a body on surface of earth is 12.6 N. When it is raised to a height half the radius of earth its weight will be

• 2.8 N

• 5.6 N

• 12.5 N

• 25.2 N