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

97.

Three equal weights of 3 kg each are hanging on a string passing over a frictionless pulley as shown in figure. The tension in the string between masses  II  and  III  will be ( Take  g = 10 m/sec² )

 

• 5 N

• 6 N

• 10 N

• 20 N

Assertion:  Impulsive  force  is  large  and  acts  for a short time.

Reason: Finite  change  in  momentum  should  be  produced  by  the  force.

• 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

Side of an equilateral triangle is l. Three point masses each of magnitude m, are placed at the three vertices of the triangle. Moment of inertia of this system about one side of the triangle as axis is given by

• $\frac{3\mathrm{m} {\mathrm{l}}^2}{4}$

• $\frac{4}{3}{\mathrm{ml}}^2$

• $\frac{3}{2}{\mathrm{ml}}^2$

• $\frac{2}{3}{\mathrm{ml}}^2$

In the diagram shown below all three rods are of equal length Land equal mass M. The system is rotated such that rod B is the axis. What is the moment of inertia of the system?

• $\frac{{\mathrm{ML}}^2}{6}$

• $\frac{4}{3}$ML²

• $\frac{{\mathrm{ML}}^2}{3}$

• $\frac{2}{3} {\mathrm{ML}}^2$