## MCQs on Rotatory and Circular Motion

Get here to see solved Multiple Choice Questions of Rotatory and Circular Motion included in the new course of Physics for Grade 11.

## Choose the best possible answer.

- The angular speed in radians/hours for daily rotation of our earth is

(a) 2π | (b) 4π | (c) π/6 | (d) π/12 |

**Solution:**In the complete rotation, the earth traverses an angular displacement, θ = 2π rad

Time taken in a complete rotation = 24 hrs

Therefore, angular speed of the earth,

- Linear acceleration is a = rα when θ is

(a) 0° | (b) 180° | (c) 360° | (d) 90° |

**Solution**Relation of linear and angular acceleration is Its magnitude is rα sinθ. For 90

^{o}, sin 90

^{o}= 1, therefore, a=rα

- What is moment of inertia of a sphere?

(a) MR^{2} | (b) 1/2 MR^{2} | (c) 2/5 MR^{2} | 1/2 M^{2}R |

(a) Linear momentum is constant | (b) Velocity is constant |

(c) It moves in a circular path | (d) Particle moves in straight line |

Explanation:As the applied force is perpendicular to the velocity of the particle at any instant of time this indicates the force is centripetal which compels the particle to move in a circular path. |

(a) Constant acceleration | (b) Constant retardation |

(c) Variable acceleration | (d) Variable speed and constant velocity |

**Explanation:**When a body is moving in circular path, its direction changes at every point. Since change in direction is accompanied by a change in the acceleration on every point, therefore, the body moving in a circle has variable acceleration.

(6) Astronauts appear weightless in space because,

(a) There is no gravity in space

(b) There is no floor pushing upwards

(c) __Satellite is freely falling__

(d) There is no air in space

**Explanation:** Freefall is motion of a body under the single force of gravity. When a satellite is revolving around the planet it is in fact in freefall towards the planet. However, the combined effect of its velocity v and gravitational force ends up it to move in a circular orbit.

(a) Velocity | (b) Kinetic Energy |

(c) Angular momentum | (d) Potential Energy |

**Explanation:**Since angular momentum,

Mass and velocity of the satellite is constant and radius r is constant for circular motion. Therefore, mvr (= angular momentum) is constant.

(Note that in the elliptical path of the satellite, when the radius r increases, there is a corresponding decrease in the velocity of the satellite and vice versa).

(a) Decrease | (b) Remains unchanged |

(c) Increase | (d) Become zero |

**Explanation:**Equator can be assumed a line drawn around the earth at the center. We know the earth is not a perfect spherical shape. It is a little expanded at the equator. Therefore, the radial distance from the center is more at the equator. An ultimate result is the particles on the equator covers more distance in one revolution as compared to the particle near the poles. More distance means larger linear velocity and larger centrifugal force. Consequently, the centripetal force is also larger at the equator. Therefore, if the earth stops suddenly, the value of g will increase at the equator.

Note that on the poles, there would be no change in the value of ‘g’ because the linear velocity of point on the pole is zero/minimum. ‘

(9) If solid sphere and solid cylinder of same mass and density rotate about their own axes, the moment of inertia will be greater for:

(a) Solid sphere

(b) __Solid cylinder__

(c) The one that has the largest mass arrives first

(d) The one that has the largest radius arrives first

**Solution: **We know that

For sphere, moment of inertia is

For cylinder, moment of inertia is

Divide (2) by (1)

Therefore, moment of inertia of cylinder is greater than the moment of inertia of the sphere.

(10) The gravitational force on an astronaut on earth’s surface is 650 N down. When she is in the international space station, is the gravitational force on her,

(a) Larger

(b) Exactly the same

(c) **Smaller**

(d) Nearly but not exactly zero

(e) Exactly zero

**Solution: **Gravitational force depends upon the distance between two bodies; in fact inversely proportional to the square of the distance between the two bodies. For the distance to be larger, the force will be smaller.

(The distance of international space station from the earth is about 408 km. Try to find the decrease in the weight of the astronaut. You can assume some mass for the astronaut as well).

A solid cylinder of mass ‘M’ and radius ‘R’ rolls down an incline without slipping. Its moment of inertia about an axis through the center of mass is MR^{2}/2. At any instant while in motion, its rotational K.E about its center of mass is what fraction of its total kinetic energy?

(a) 1/2 | (b) 1/4 | (c) 1/3 | (d) 2/5 | (e>Non of these |

**Solution:** We know that

Total K.E = Rotational K.E + Translational

The rotational energy as fraction of total energy is,

Therefore, (C) is correct option.