Uniform circular motion; angular velocity and centripetal acceleration — NEET & JEE Questions

Question 1 · difficulty L1 · recall

For uniform circular motion with speed v and radius r, centripetal acceleration has magnitude

• A. $v^2/r$
• B. $vr$
• C. $v/r^2$
• D. $r/v^2$

Question 2 · 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 3 · 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 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. $$\frac{\mu}{\sqrt{r g}}$$