Angular Displacement

Q. An athlete running with constant speed, completes one round of a circular track of radius $R$ in $40\text{seconds}$. What will be his angular displacement at the end of $20\text{seconds}$?

1. $\frac{\pi }{2}\text{rad}$
2. $\frac{\pi }{3}\text{rad}$
3. $\frac{\pi }{4}\text{rad}$
4. $\pi \text{rad}$

Q. A person covers $\frac{1}{3}rd$ of a circle of radius $10\text{m}$. Calculate angular displacement in radians & degrees.

1. $\frac{\pi }{3}\text{rad},{60}^{\circ }$
2. $\pi \text{rad},{180}^{\circ }$
3. $\frac{\pi }{4}\text{rad}.{45}^{\circ }$
4. $\frac{2\pi }{3}\text{rad},{120}^{\circ }$

Q. If a merry-go-round is rotating in the clockwise direction, then its angular displacement is pointing upwards from the centre of rotation.

1. False
2. True

Q. Which of the following statements is true about angular displacement?

1. It has a unit, but no dimension.
2. It has a dimension, but no unit.
3. It neither has unit nor dimension.
4. It has both unit as well as dimension.

Q. A particle moves in a circle of radius R in such a way its tangential acceleration is always equal to radial acceleration. Distance travelled by the particle before its speed is doubled from v₀ to 2v₀, is

एक कण R त्रिज्या के वृत्त में इस प्रकार गति करता है कि इसका स्पर्शरेखीय त्वरण सदैव त्रिज्य त्वरण के बराबर हो। कण की चाल के v₀ से 2v₀ तक दोगुनी होने से पहले इसके द्वारा तय की गई दूरी है

1. 2R ln(2)
   
2. R ln(2)
   
3. πR ln(2)
   
4. $\frac{\pi R}{\ln \left(2\right)}$
   

Q. A boy running on a circular track of radius $10\text{m}$ completes $3$ revolution and comes back to the point from where he started. Calculate the angular displacement of the boy $\left(\text{in rad}\right)$.

1. $3\pi$
2. $6\pi$
3. $0$
4. $\frac{\pi }{3}$

Q. The instantaneous angular position of a point on a rotating wheel is given by the equation $\theta \left(t\right)=3t^3-9t^2$ (Here $t$ is in seconds). The angular acceleration of the wheel becomes zero at

1. $t=1\text{s}$
2. $t=0.5\text{s}$
3. $t=0.25\text{s}$
4. $t=2\text{s}$

Q. A car wheel is rotated to uniform angular acceleration about its axis. Initially its angular velocity is zero. It rotates through an angle ${\theta }_1$ in the first $2$s. In the next $2$ s, it rotates through an additional angle ${\theta }_2$, the ratio of $\frac{{\theta }_2}{{\theta }_1}$ is

1. 1
2. 2
3. 3
4. 4

Q. The magnitude of the displacement of a particle moving in a circle of radius $a$ with constant angular speed $\omega$ varies with time $t$ as

1. $2asin\omega t$
2. $2asin\frac{\omega t}{2}$
3. $2acos\omega t$
4. $2acos\frac{\omega t}{2}$

Q. If a merry-go-round is rotating in the clockwise direction, then its angular displacement is pointing upwards from the centre of rotation.

1. False
2. True

Q. Find the angular displacement of the hour hand of a normal clock in $4\text{h}$

1. $\frac{\pi }{3}$
2. $\frac{\pi }{6}$
3. $\frac{2\pi }{3}$
4. $\frac{3\pi }{2}$

Q. Assume that the earth goes round the sun in a circular orbit with a constant speed of ${\text{30 km s}}^{-1}$. Which of the following is correct?

1. The average velocity of the earth from 1st Jan., 90 to 30 th June, 90 is zero.
2. The average acceleration during the above period is $60{\text{km s}}^{-2}$.
3. The average speed from 1st Jan., 90 to 31st Dec., 90 is zero.
4. The instantaneous acceleration of the earth points towards the sun.

Q. Assume that the earth goes round the sun in a circular orbit with a constant speed of ${\text{30 km s}}^{-1}$. Which of the following is correct?

1. The average velocity of the earth from 1st Jan., 90 to 30 th June, 90 is zero.
2. The average acceleration during the above period is $60{\text{km s}}^{-2}$.
3. The average speed from 1st Jan., 90 to 31st Dec., 90 is zero.
4. The instantaneous acceleration of the earth points towards the sun.

Q. Two strings are tied $2\text{m}$ apart on a rod and on the other end a mass $200\text{g}$ is tied as shown in figure. Each string is $1.25\text{m}$ long. FInd the tensions $T_1$ and $T_2$ if the rod is rotated with $60\text{rpm}$. Consider ${\pi }^2=10$

1. $6\text{N},3\text{N}$
2. $6.25\text{N},3.75\text{N}$
3. $4.25\text{N},5.75\text{N}$
4. $5.25\text{N},4.75\text{N}$