Velocity in 2D

Q. A circular disc with a groove along its diameter is placed horizontally. A block of mass $1\text{kg}$ is placed as shown. The coefficient of friction between the block and all surfaces of groove in contact is $\mu =\frac{2}{5}$. The disc has an acceleration of $25\text{m}/s^2$ Find the acceleration of the block with respect to disc.

1. $10\text{m}/s^2$
2. $20\text{m}/s^2$
3. $15\text{m}/s^2$
4. $5\text{m}/s^2$

Q. In a situation shown below, if the length of seconds hand is $\frac{30}{\pi }\text{cm}$, find the magnitude of change in velocity of the tip of the seconds hand.

1. $1.732\text{cm/s}$
2. $2\text{cm/s}$
3. $1.414\text{cm/s}$
4. $0\text{cm/s}$

Q. In a gravity free room a man of mass $m_1$ is standing at a height $h$ above the floor. He throws a ball of mass $m_2$ vertically downwards with a speed $u$. Find the distance of the man from the floor when the ball reaches the ground.
(Neglect the height of the man)

1. $\left(\frac{m_1+m_2}{m_1-m_2}\right)h$
2. $\frac{h}{m_1}$
3. $(1+\frac{m_2}{m_1})h$
4. $\frac{m_2}{m_1}h$

Q.

A river is flowing with a speed of 1 km/hr. A swimmer wants to go to point ‘C’ starting from ‘A’. He swims with a speed of 5 km/hr at an angle $\theta$ w.r.t the river flow. If AB =BC =400 m, what is the value of $\theta$?

1. ${37}^{\circ }$

2. ${53}^{\circ }$

3. ${30}^{\circ }$

4. ${60}^{\circ }$

Q. A particle moves according to the equation $x=t^2+3t+4$ . The average velocity in the first $5\text{s}$ is

1. $8{\text{ms}}^{-1}$
2. $7.6{\text{ms}}^{-1}$
3. $6.4{\text{ms}}^{-1}$
4. $5.8{\text{ms}}^{-1}$

Q. The seconds hand of a watch has length $6\text{cm}$. Speed of end point and magnitude of difference of velocities at two perpendicular positions will be

1. $2\pi$ and $0\text{mm/s}$
2. $2\sqrt{2}\pi$ and $4.44\text{mm/s}$
3. $2\sqrt{2}\pi$ and $2\pi \text{mm/s}$
4. $2\pi$ and $2\sqrt{2}\pi \text{mm/s}$