The quantities RC and $\left(\frac{\mathrm{L}}{\mathrm{R}}\right)$ (where R, L and C stand for resistance, inductance and capacitance respectively) have the dimensions of

• force

• linear momentum

• linear acceleration

• time

The number of significant figures in 0.002305 is

• 6

• 4

• 7

• 2

A body travelling with uniform acceleration crosses two points A and B with velocities 20 ms^-1 and 30 ms^-1 respectively. The speed of the body at the mid-point of A and B is nearest to

• 25.5 ms^-1

• 25 ms^-1

• 24 ms^-1

• $10\sqrt{6} {\mathrm{ms}}^{-1}$

An aeroplane flies around a square field ABCD of each side 1000 km. Its speed along AB is 250 kmh^-1, along BC 500 kmh^-1, along CD 200 kmh^-1 and along DA 100 kmh^-1. Its average speed (in kmh^-1)over the entire trip is

• 225.5

• 175.5

• 190.5

• 310.5

Free fall of an object (in vacuum) is a case of motion with

• uniform velocity

• uniform acceleration

• variable acceleration

• constant momentum

The maximum height of a projectile is half of its range on the- horizontal. If the velocity of projection is u, its range on the horizontal is

• $\frac{2{\mathrm{u}}^2}{5\mathrm{g}}$

• $\frac{3{\mathrm{u}}^2}{5\mathrm{g}}$

• $\frac{4{\mathrm{u}}^2}{5\mathrm{g}}$

• $\frac{{\mathrm{u}}^2}{5\mathrm{g}}$

7.

A stone of mass 2 kg is tied to a string of length 0.5 m. If the breaking tension of the string is 900 N, then the maximum angular velocity, the stone can have in uniform circular motion is

• 30 rad s^-1

• 20 rad s^-1

• 10 rad s^-1

• 25 rad s^-1

The position of a particle is given by $\overrightarrow{\mathrm{r}} = 2{\mathrm{t}}^2 \hat{\mathrm{i}} + 3\mathrm{t} \hat{\mathrm{j}} + 4 \hat{\mathrm{k}}$, where t is in second and the coefficients have proper units for $\overrightarrow{\mathrm{r}}$ to be in metre. The $\overrightarrow{\mathrm{a}} \left(\mathrm{t}\right)$ of the particle at t = 1 s is

• 4 ms^-2 along y-direction

• 3 ms^-2 along x-direction

• 4 ms^-2 along x-direction

• 2 ms^-2 along z-direction

A passenger getting down from a moving bus, falls in the direction of the motion of the bus. This is an example for

• moment of inertia

• second law of motion

• inertia of motion

• inertia of rest

A body of mass 6 kg is hanging from another body of mass 10 kg as shown in figure. This combination is being pulled up by a string with an acceleration of 2 ms^-2. The tension T₁ is, (g =10 ms^-2)

• 240 N

• 150 N

• 220 N

• 192 N