Motion in a Plane Questions and Answers Part-14

1. A weightless thread can bear tension upto 3.7 kg wt. A stone of mass 500 gms is tied to it and revolved in a circular path of radius 4 m in a vertical plane. If \[g=10ms^{-2}\]  , then the maximum angular velocity of the stone will be
a) 4 radians/sec
b) 16 radians/sec
c) \[\sqrt{21}\]  radians/sec
d) 2 radians/sec

Answer: a

2. The maximum velocity at the lowest point, so that the string just slack at the highest point in a vertical circle of radius l
a) \[\sqrt{gl}\]
b) \[\sqrt{3gl}\]
c) \[\sqrt{5gl}\]
d) \[\sqrt{7gl}\]

Answer: c
Explanation: \[\sqrt{5gl}\]

3. If the equation for the displacement of a particle moving on a circular path is given by \[\left(\theta\right)=2t^{3}+0.5\]   , where \[\theta\] is in radians and t in seconds, then the angular velocity of the particle after 2 sec from its start is
a) 8 rad/sec
b) 12 rad/sec
c) 24 rad/sec
d) 36 rad/sec

Answer: c

4. A body of mass m hangs at one end of a string of length l, the other end of which is fixed. It is given a horizontal velocity so that the string would just reach where it makes an angle of \[60^{\circ}\] with the vertical. The tension in the string at mean position is
a) 2mg
b) mg
c) 3mg
d) \[\sqrt{3}\] mg

Answer: a

5. In a vertical circle of radius r, at what point in its path a particle has tension equal to zero if it is just able to complete the vertical circle
a) Highest point
b) Lowest point
c) Any point
d) At a point horizontally from the centre of circle of radius r

Answer: a
Explanation: Highest point

6. The tension in the string revolving in a vertical circle with a mass m at the end which is at the lowest position
a) \[\frac{mv^{2}}{r}\]
b) \[\frac{mv^{2}}{r}-mg\]
c) \[\frac{mv^{2}}{r}+mg\]
d) mg

Answer: c

7. A hollow sphere has radius 6.4 m. Minimum velocity required by a motor cyclist at bottom to complete the circle will be
a) 17.7 m/s
b) 10.2 m/s
c) 12.4 m/s
d) 16.0 m/s

Answer: a

8. A pendulum bob on a 2 m string is displaced \[60^{\circ}\] from the vertical and then released. What is the speed of the bob as it passes through the lowest point in its path
a) \[\sqrt{2}\] m/s
b) \[\sqrt{9.8}\] m/s
c) 4.43 m/s
d) \[1/\sqrt{2}\] m/s

Answer: c

9. A fan is making 600 revolutions per minute. If after some time it makes 1200 revolutions per minute, then increase in its angular velocity is
a) \[10\pi rad \diagup sec\]
b) \[20\pi rad \diagup sec\]
c) \[40\pi rad \diagup sec\]
d) \[60\pi rad \diagup sec\]

Answer: b

10. A particle is tied to 20cm long string. It performs circular motion in vertical plane. What is the angular velocity of string when the tension in the string at the top is zero
a) 5 rad/sec
b) 2 rad/sec
c) 7.5 rad/sec
d) 7 rad/sec

Answer: d