If 2 kg mass is rotating on a circular path of radius 0.8 m with angular velocity of 44 rad/sec. If radius of the path becomes 1 m, ther what will be the value of angular velocity?

• 28.16 rad/sec

• 19.28 rad/sec

• 8.12 rad/sec

• 35.26 rad/sec

A solid cylinder, a circular disc, a solid sphere and a hollow cylinder of the same radius are placed on an inclined plane. Which of the following will have maximum acceleration at the bottom of the plane?

• Circular disc

• Solid cylinder

• Solid sphere

• Hollow cylinder

Calculate the heat emitted by a bulb of 100 W in 1 min.

• 100 J

• 1000 J

• 600 J

• 6000 J

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

175.

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

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

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

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

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

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

What is moment of inertia of a cylinder of radius r, along its height?

• mr²

• mr²/2

• 2 mr²/5

• mr²/5

Four holes of radius Rare cut from a thin square plate of side 4R and mass M. The moment of inertia of the remaining portion about z-axis is

• $\frac{\mathrm{\pi }}{12} {\mathrm{MR}}^2$

• $\left(\frac{4}{3} - \frac{\mathrm{\pi }}{4}\right) {\mathrm{MR}}^2$

• $\left(\frac{4}{3} - \frac{\mathrm{\pi }}{6}\right) {\mathrm{MR}}^2$

• $\left(\frac{8}{3} - \frac{10\mathrm{\pi }}{16}\right) {\mathrm{MR}}^2$

Which of the following pairs does not have same dimensions ?

• impulse and momentum

• moment of inertia and moment of force

• angular momentum and Planck's constant

• work and torque

Assertion:  A hollow shaft is found to be stronger than a solid shaft made of same material. 

Reason:  The torque required to produce a given twist in hollow cylinder is greater than that required to twist a solid cylinder of same size and material.

• If both assertion and reason are true and reason is the 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