What is the moment of inertia for a solid sphere w.r.t. a tangent touching to its surface?

• 2/5 MR²

• 7/5 MR²

• 2/3 MR²

• 5/3 MR²

Water is flowing with velocity 4 m s^-1 in a cylinder of diameter 8 cm, it is connected to a pipe with it end tip of diameter 2 cm, calculate the velocity of water at this free end.

• 4 m s^-1

• 8 m s^-1

• 32 m s^-1

• 64 m s^-1

A cylindrical wire is twisted with an angle θ, what is torsion produced in it?

• $\frac{\mathrm{C}}{\mathrm{\theta }}$

• Cθ

• $\frac{\mathrm{C}}{{\mathrm{\theta }}^2}$

• Cθ^3/2

4.

Given  $\overrightarrow{\mathrm{\omega }} = 2 \hat{\mathrm{k}}$  and  $\overrightarrow{\mathrm{r}} = 2 \hat{\mathrm{i}} + 2 \hat{\mathrm{j}}$. Find the linear velocity.

• $4\hat{\mathrm{i}} + 4 \hat{\mathrm{j}}$

• $4 \hat{\mathrm{i}} + 4 \hat{\mathrm{j}}$

• $-4 \hat{\mathrm{i}} + 4 \hat{\mathrm{j}}$

• $- 4 \hat{\mathrm{i}} - 4 \hat{\mathrm{j}}$

If maximum speed in SHM is given by V_m, what is its average speed?

• $\frac{\mathrm{\pi }}{2}$ V_m

• $\frac{2}{\mathrm{\pi }}$ V_m

• $\frac{\mathrm{\pi }}{4}$ V_m

• $\frac{{\mathrm{V}}_{\mathrm{m}}}{\sqrt{2}}$

A 0.2 kg object at rest is subjected to a force  $\left(0.3 \hat{\mathrm{i}} - 0.4 \hat{\mathrm{j}}\right)$N. What is the velocity after 6 s?

• $\left( 9 \hat{\mathrm{i}} - 12 \hat{\mathrm{j}} \right)$

• $\left( 8 \hat{\mathrm{i}} - 16 \hat{\mathrm{j}} \right)$

• $\left(12 \hat{\mathrm{i}} - 9 \hat{\mathrm{j}} \right)$

• $\left( 16 \hat{\mathrm{i}} - 8 \hat{\mathrm{j}} \right)$

If man were standing unsymmetrically between parallel cliffs, claps his hands and starts hearing a series of echoes at intervals of 1 s. If speed of sound in air is 340 ms', the distance between two cliffs would be

• 340 m

• 510 m

• 170 m

• 680 m

Half life of a radioactive material is 5 years, then the percentage of it remained after 25 years will be

• 3.125%

• 6.25%

• 1.25%

• 25%

Assertion: Total energy is conserved in moving a satellite to higher orbit. 

Reason:  Sum of change in PE and KE is same in magnitude and opposite in nature.

• If both assertion and reason are true and reason is correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false.

• If both assertion and reason are false.

Assertion: KE is conserved at every instant of (elastic) collision.
Reason: No deformation of matter occurs in elastic collision.

• If both assertion and reason are true and reason is correct explanation of assertion.

• If both assertion and reason are true but reason is not correct explanation of assertion.

• If assertion is true but reason are false.

• If both assertion and reason are false.