Motion in a Plane Questions and Answers Part-1

1. If the body is moving in a circle of radius r with a constant speed v , its angular velocity is
a) \[V^{2}\diagup r\]
b) vr
c) \[V\diagup r\]
d) \[r\diagup v\]

Answer: c

2. Two racing cars of masses \[m_{1} and m_{2}\]   are moving in circles of radii \[r_{1} and r_{2}\]   respectively. Their speeds are such that each makes a complete circle in the same duration of time t . The ratio of the angular speed of the first to the second car is
a) \[m_{1} :m_{2}\]
b) \[r_{1} :r_{2}\]
c) \[1 :1\]
d) \[m_{1}r_{1}:m_{2}r_{2}\]

Answer: c

3. A cyclist turns around a curve at 15 miles/hour. If he turns at double the speed, the tendency to overturn is
a) Doubled
b) Quadrupled
c) Halved
d) Unchanged

Answer: b

4. A body of mass m is moving in a circle of radius r with a constant speed v . The force on the body is \[\frac{mv^{2}}{r}\] and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle
a) \[\frac{mv^{2}}{r}\times\pi r\]
b) Zero
c) \[\frac{mv^{2}}{r^{2}}\]
d) \[\frac{\pi r^{2}}{mv^{2}}\]

Answer: b
Explanation: Work done by centripetal force is always zero

5. If a particle moves in a circle describing equal angles in equal times, its velocity vector
a) Remains constant
b) Changes in magnitude
c) Changes in direction
d) Changes both in magnitude and direction

Answer: c
Explanation: It is always directed in a direction of tangent to circle

6. A stone of mass m is tied to a string of length l and rotated in a circle with a constant speed v . If the string is released, the stone flies
a) Radially outward
b) Radially inward
c) Tangentially outward
d) With an acceleration \[\frac{mv^{2}}{l}\]

Answer: c
Explanation: Stone flies in the direction of instantaneous velocity due to inertia

7. A body is moving in a circular path with a constant speed. It has
a) A constant velocity
b) A constant acceleration
c) An acceleration of constant magnitude
d) An acceleration which varies with time

Answer: c

8. A motor cyclist going round in a circular track at constant speed has
a) Constant linear velocity
b) Constant acceleration
c) Constant angular velocity
d) Constant force

Answer: c
Explanation: Linear velocity, acceleration and force varies in direction.

9. A car moving on a horizontal road may be thrown out of the road in taking a turn
a) By the gravitational force
b) Due to lack of sufficient centripetal force
c) Due to rolling frictional force between tyre and road
d) Due to the reaction of the ground

Answer: b
Explanation: Due to lack of sufficient centripetal force

10. Two particles of equal masses are revolving in circular paths of radii \[r_{1} and r_{2}\]   respectively with the same speed. The ratio of their centripetal forces is
a) \[\frac{r_{2}}{r_{1}}\]
b) \[\sqrt{\frac{r_{2}}{r_{1}}}\]
c) \[\left(\frac{r_{1}}{r_{2}}\right)^{2}\]
d) \[\left(\frac{r_{2}}{r_{1}}\right)^{2}\]

Answer: a