## Motion in a Plane Questions and Answers Part-7

1. The angular speed of seconds needle in a mechanical watch is
a) $\frac{\pi}{30}rad\diagup s$
b) $2\pi rad\diagup s$
c) $\pi rad\diagup s$
d) $\frac{\pi}{60}rad\diagup s$

Explanation: 2. The angular velocity of a particle rotating in a circular orbit 100 times per minute is
c) 10.47 deg/s
d) 60 deg/s

Explanation: 3. A body of mass 100 g is rotating in a circular path of radius r with constant velocity. The work done in one complete revolution is
a) 100 rJ
b) $\left(r\diagup100\right) J$
c) (100/r) J
d) Zero

Explanation: Work done in circular motion is always zero

4. A particle comes round a circle of radius 1 m once. The time taken by it is 10 sec. The average velocity of motion is
a) $0.2\pi m\diagup s$
b) $2\pi m\diagup s$
c) $2m\diagup s$
d) Zero

Explanation: In complete revolution total displacement is zero so average velocity is zero

5. An unbanked curve has a radius of 60m . The maximum speed at which a car can make a turn if the coefficient of static friction is 0.75, is
a) $2.1 m\diagup s$
b) $14 m\diagup s$
c) $21 m\diagup s$
d) $7 m\diagup s$

Explanation: 6. A wheel completes 2000 revolutions to cover the 9.5 km. distance. then the diameter of the wheel is
a) 1.5 m
b) 1.5 cm
c) 7.5 cm
d) 7.5 m

Explanation: Distance covered in ‘n’ revolution = n 2 $\pi$ r = n $\pi$ D
2000 $\pi$ D = 9500 [As n = 2000, distance = 9500 m]
$D = \frac{9500}{2000\times\pi} = 1.5 m$

7. A cycle wheel of radius 0.4 m completes one revolution in one second then the acceleration of a point on the cycle wheel will be
a) $0.8 m\diagup s^{2}$
b) $0.4 m\diagup s^{2}$
c) $1.6\pi^{2} m\diagup s^{2}$
d) $0.4\pi^{2} m\diagup s^{2}$

Explanation: Centripetal acceleration = 8. The centripetal acceleration is given by
a) $v^{2} \diagup r$
b) vr
c) $vr^{2}$
d) $v \diagup r$

Explanation: $v^{2} \diagup r$

9. A cylindrical vessel partially filled with water is rotated about its vertical central axis. It’s surface will
a) Rise equally
b) Rise from the sides
c) Rise from the middle
d) Lowered equally

b) Change in K.E. is 1/2 $mv^{2}$
c) Change in K.E. is $mv^{2}$ 