Motion in a Plane Questions and Answers Part-12

1. A mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity \[\omega_{0}\] . If the length of the string and angular velocity are doubled, the tension in the string which was initially \[T_{0}\] is now
a) \[T_{0}\]
b) \[T_{0}\diagup 2\]
c) \[4T_{0}\]
d) \[8T_{0}\]

Answer: d

2. A particle is moving in a circle of radius R with constant speed v, if radius is double then its centripetal force to keep the same speed should be
a) Doubled
b) Halved
c) Quadrupled
d) Unchanged

Answer: b

3. A stone ties to the end of a string 1m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolution in 44m seconds, what is the magnitude and direction of acceleration of the stone
a) \[\frac{\pi^{2}}{4}ms^{-2}\]  and direction along the radius towards the centre
b) \[\pi^{2}ms^{-2}\]  and direction along the radius away from the centre
c) \[\pi^{2}ms^{-2}\]  and direction along the radius towards the centre
d) \[\pi^{2}ms^{-2}\]  and direction along the tangent to the circle

Answer: c

4. A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of 0.5 m/s. What is the height of the plane of circle from vertex of the funnel ?
a) 0.25 cm
b) 2 cm
c) 4 cm
d) 2.5 cm

Answer: d

5. What is the angular velocity of earth
a) \[\frac{2\pi}{86400}rad\diagup sec\]
b) \[\frac{2\pi}{3600}rad\diagup sec\]
c) \[\frac{2\pi}{24}rad\diagup sec\]
d) \[\frac{2\pi}{6400}rad\diagup sec\]

Answer: a

6. If the length of the second's hand in a stop clock is 3 cm the angular velocity and linear velocity of the tip is
a) 0.2047 rad/sec., 0.0314 m/sec
b) 0.2547 rad/sec., 0.314 m/sec
c) 0.1472 rad/sec., 0.06314 m/sec
d) 0.1047 rad/sec., 0.00314 m/sec

Answer: d

7. In a circus stuntman rides a motorbike in a circular track of radius R in the vertical plane. The minimum speed at highest point of track will be
a) \[\sqrt{2gR}\]
b) \[2gR\]
c) \[\sqrt{3gR}\]
d) \[\sqrt{gR}\]

Answer: d

8. A block of mass m at the end of a string is whirled round in a vertical circle of radius R . The critical speed of the block at the top of its swing below which the string would slacken before the block reaches the top is
a) Rg
b) \[\left(Rg\right)^{2}\]
c) \[R\diagup g\]
d) \[\sqrt{Rg}\]

Answer: d

9. A sphere is suspended by a thread of length l . What minimum horizontal velocity has to be imparted the ball for it to reach the height of the suspension
a) gl
b) 2gl
c) \[\sqrt{gl}\]
d) \[\sqrt{2gl}\]

Answer: d

10. A bottle of sodawater is grasped by the neck and swing briskly in a vertical circle. Near which portion of the bottle do the bubbles collect
a) Near the bottom
b) In the middle of the bottle
c) Near the neck
d) Uniformly distributed in the bottle

Answer: c
Explanation: Due to less centrifugal force experienced by the bubbles.