Motion in a Plane Questions and Answers Part-6

1. A 500 kg car takes a round turn of radius 50 m with a velocity of 36 km/hr. The centripetal force is
a) 250 N
b) 750 N
c) 1000 N
d) 1200 N

Answer: c

2. A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved
a) 14 m/s
b) 3 m/s
c) 3.92 m/s
d) 5 m/s

Answer: a

3. A body of mass 5 kg is moving in a circle of radius 1m with an angular velocity of 2 radian/sec. The centripetal force is
a) 10 N
b) 20 N
c) 30 N
d) 40 N

Answer: b

4. If a particle of mass m is moving in a horizontal circle of radius r with a centripetal force \[\left(-k\diagup r^{2}\right)\] , the total energy is
a) \[-\frac{k}{2r}\]
b) \[-\frac{k}{r}\]
c) \[-\frac{2k}{r}\]
d) \[-\frac{4k}{r}\]

Answer: a

5. A stone of mass of 16 kg is attached to a string 144 m long and is whirled in a horizontal circle. The maximum tension the string can withstand is 16 Newton. The maximum velocity of revolution that can be given to the stone without breaking it, will be
a) \[20ms^{-1}\]
b) \[16ms^{-1}\]
c) \[14ms^{-1}\]
d) \[12ms^{-1}\]

Answer: d

6. A circular road of radius 1000 m has banking angle 45o . The maximum safe speed of a car having mass 2000 kg will be, if the coefficient of friction between tyre and road is 0.5
a) 172 m/s
b) 124 m/s
c) 99 m/s
d) 86 m/s

Answer: a

7. The second's hand of a watch has length 6 cm.Speed of end point and magnitude of difference of velocities at two perpendicular positions will be
a) 6.28 and 0 mm/s
b) 8.88 and 4.44 mm/s
c) 8.88 and 6.28 mm/s
d) 6.28 and 8.88 mm/s

Answer: d

8. A sphere of mass m is tied to end of a string of length l and rotated through the other end along a horizontal circular path with speed v . The work done in full horizontal circle is
a) 0
b) \[\left(\frac{mv^{2}}{l}\right).2\pi l\]
c) \[mg.2\pi l\]
d) \[\left(\frac{mv^{2}}{l}\right).\left( l\right)\]

Answer: a
Explanation: Work done by centripetal force in uniform circular motion is always equal to zero

9. A body is whirled in a horizontal circle of radius 20 cm. It has angular velocity of 10 rad/s. What is its linear velocity at any point on circular path
a) 10 m/s
b) 2 m/s
c) 20 m/s
d) \[\sqrt{2}\] m/s

Answer: b

10. Find the maximum velocity for skidding for a car moved on a circular track of radius 100 m. The coefficient of friction between the road and tyre is 0.2
a) 0.14 m/s
b) 140 m/s
c) 1.4 km/s
d) 14 m/s

Answer: d