Uniform circular motion; angular velocity and centripetal acceleration — practice questions

Question 1 · difficulty L2 · understanding

A particle of charge $1.6 \mu \mathrm{C}$ and mass $16 \mu \mathrm{~g}$ is present in a strong magnetic field of 6.28 T . The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is _________ s. $(\pi=3.14)$

Question 2 · difficulty L2 · understanding

A stone tied to $180 \mathrm{~cm}$ long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is $\frac{1936}{x} ms^{-2}$. The value of $x$ ________. (Take $\pi=\frac{22}{7}$ )

Question 3 · difficulty L2 · understanding

A person starts his journey from centre 'O' of the park and comes back to the same position following path OPQO as shown in the figure. The radius of path taken by the person is 200 m and he takes 3 min 58 sec to complete his journey. The average speed of the person is _____________ ms $$-$$1 . (take $$\pi$$ = 3.14)

Question 4 · difficulty L2 · understanding

A 0.5 kg mass is in contact against the inner wall of a cylindrical drum of radius 4 m rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is 5 rad/s. The coefficient of friction between the drum’s inner wall surface and mass is _________. (Take $g = 10\ \mathrm{m/s^2}$)

• A. 0.1
• B. 0.5
• C. 0.7
• D. 0.3

Question 5 · difficulty L2 · understanding

Two cars A and B each of mass $10^3$ kg are moving on parallel tracks separated by a distance of 10 m, in same direction with speeds 72 km/h and 36 km/h. The magnitude of angular momentum of car A with respect to car B is ________ J·s.

• A. $3.6 \times 10^{5}$
• B. $10^{5}$
• C. $3 \times 10^{5}$
• D. $2 \times 10^{5}$

Question 6 · difficulty L2 · understanding

A sportsman runs around a circular track of radius $r$ such that he traverses the path $A B A B$. The distance travelled and displacement, respectively, are

• A. $\pi r, 3 r$
• B. $2 \mathrm{r}, 3 \pi \mathrm{r}$
• C. $3 \pi \mathrm{r}, 2 \mathrm{r}$
• D. $3 \pi r, \pi r$

Question 7 · difficulty L2 · understanding

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius $$9 \mathrm{~m}$$ and completes 120 resolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in $$\mathrm{m} / \mathrm{s}^2$$ ) :

• A. $$4 \pi^2 \mathrm{~ms}^{-2}$$
• B. $$16 \pi^2 \mathrm{~ms}^{-2}$$
• C. $$57600 \pi^2 \mathrm{~ms}^{-2}$$
• D. Zero

Question 8 · difficulty L2 · understanding

A cyclist starts from the point $$P$$ of a circular ground of radius $$2 \mathrm{~km}$$ and travels along its circumference to the point $$\mathrm{S}$$. The displacement of a cyclist is:

• A. $$\sqrt8$$ km
• B. 4 km
• C. 6 km
• D. 8 km

Question 9 · difficulty L2 · understanding

A ball of mass $0.5 \mathrm{~kg}$ is attached to a string of length $50 \mathrm{~cm}$. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is $400 \mathrm{~N}$. The maximum possible value of angular velocity of the ball in $\mathrm{rad} / \mathrm{s}$ is, :

• A. 1600
• B. 20
• C. 40
• D. 1000

Question 10 · difficulty L2 · understanding

A coin is placed on a disc. The coefficient of friction between the coin and the disc is $$\mu$$. If the distance of the coin from the center of the disc is $$r$$, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is :

• A. $$\sqrt{\frac{r}{\mu g}}$$
• B. $$\sqrt{\frac{\mu g}{r}}$$
• C. $$\frac{\mu g}{r}$$
• D. $$\frac{\mu}{\sqrt{r g}}$$