A man wants to slide down a rope. The breaking load for the rope is $\frac{2}{3}$rd ofthe weight of the man. With what minimum acceleration should fireman slide down?

• g/4

• g/3

• 2g/3

• g/6

A glass marble projected horizontally from the top of a table falls of a distance x from the edge ofthe table. If h is the height of the table, then the velocity of projection is

• $\mathrm{h} \sqrt{\frac{\mathrm{g}}{2 \mathrm{x}}}$

• $\mathrm{x} \sqrt{\frac{\mathrm{g}}{2\mathrm{h}}}$

• gxh

• g x + h

If x = $\frac{{\mathrm{\epsilon }}_0 \mathrm{lV}}{\mathrm{t}}$is the permittivity of free space, l is length, V is potential difference and t is time. The dimensions of x are same as that of

• charge

• resistance

• voltage

• current

If the radius of the earth is reduced by 1% without changing its mass. The change in g will be

• 2% decrease

• 2% increases

• 1% decrease

• 1% increases

If a and b are two vectors, then the value of

      (a × b) × (a − b) is

• 2 (b x a)

• − 2(b x a)

• b x a

• a x b

If the change in the value of g at a height h above the surface of the earth is the same as at a depth x below in surface, then

• x = h²

• x = 0.5 h

• x = 2h

• x = h

Dimension of $\frac{\mathrm{L}}{\mathrm{RCV}}$ is

• [A^-1]

• [A^-2]

• [A]

• [A²]

The maximum range of a gun on horizontal terrain is 16 km if g = 10 m/s². What must be the muzzle velocity of the shell?

• 200 m/s

• 100 m/s

• 400 m/s

• 300 m/s

The length, breath and thickness of a block are given by l = 12 cm, b= 6 cm and t = 2.45 cm. The volume of the  block according to the idea of significant figure should be

• 1 x 10² cm²

• 2 x 10² cm³

• 1.763 x 10² cm²

• None of these

If the heat of 110 J is added to a gaseous system, whose internal energy is 40 J. Then the amount of external work done is

• 140 J

• 70 J

• 110 J

• 150 J