A particle is moving uniformly in a circular path of radius r. When it moves through an angular displacement θ, then the magnitude of the corresponding linear displacement will be

• $2\mathrm{r} \cos \left(\frac{\mathrm{\theta }}{2}\right)$

• $2\mathrm{r} \cot \left(\frac{\mathrm{\theta }}{2}\right)$

• $2\mathrm{r} \tan \left(\frac{\mathrm{\theta }}{2}\right)$

• $2\mathrm{r} \sin \left(\frac{\mathrm{\theta }}{2}\right)$

A uniform rod is suspended horizontally from its mid- point. A piece of metal whose weight is w is suspended at a distance l from the mid-point. Another weight w₁ is suspended on the other side at a distance l₁ from the mid-point to bring the rod to a horizontal position. When w is completely immersed in water, w₁ needs to be kept at a distance l₁ from the mid-point to get the rod back into horizontal position. The specific gravity of the metal piece is

• $\frac{\mathrm{w}}{{\mathrm{w}}_1}$

• $\frac{{\mathrm{wl}}_1}{\mathrm{wl} - {\mathrm{w}}_1{\mathrm{l}}_2}$

• $\frac{{\mathrm{l}}_1}{{\mathrm{l}}_1 - {\mathrm{l}}_2}$

• $\frac{{\mathrm{l}}_1}{{\mathrm{l}}_2}$

A uniform solid spherical ball is rolling down a smooth inclined plane from a height h. The velocity attained by the ball when it reaches the bottom of the inclined plane is v. If the ball is now thrown vertically upwards with the same velocity v, the maximum height to which the ball will rise is

• $\frac{5\mathrm{h}}{8}$

• $\frac{3\mathrm{h}}{5}$

• $\frac{5\mathrm{h}}{7}$

• $\frac{7\mathrm{h}}{9}$

A thin rod AB is held horizontally so that it can freely rotate in a vertical plane about the end A as shown in the figure. The potential energy of the rod when it hangs vertically is taken to be zero. The end B of the rod is released from rest from a horizontal position. At the instant the rod makes an angle θ with the horizontal

• the speed of end B is proportional to $\sqrt{\sin \mathrm{\theta }}$

• the potential energy is proportional to (1 − cos θ)

• the angular acceleration is proportional to cos θ

• the torque about A remains the same as its initial value

Two particles A and B having different masses are projected from a tower with same speed. A is projected vertically upward and B vertically downward. On reaching the ground

• velocity of A is greater than that of B

• velocity of B is greater than that of A

• both A and B attain the same velocity

• the particle with the larger mass attains higher velocity

Which of the following is scalar quantity?

• Current

• Velocity

• Force

• Acceleration