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Practice Exercise¶

The rotational K.E of hoop is
Equal to its translational K.E
Half than its translational K.E
Double than its translational K.E
Four times than its translational K.E
Ans: Equal to its translational K.E
The 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 length of time. The ratio of the angular speed of the first car to that of the second car is
\(m_1\) : \(m_2\)
\(r_1\) : \(r_2\)
\(1\) : \(1\)
\(m_1r_1\) : \(m_2r_2\)
Ans: \(1\) : \(1\)
The angular velocity of the minute hand of a clock is
\(\frac{2\pi}{60} rad^{-1}\)
\(\frac{\pi}{24} rad^{-1}\)
\(\frac{2\pi}{3600} rad^{-1}\)
\(\frac{\pi}{3600} rad^{-1}\)
Ans: \(\frac{2\pi}{3600} rad^{-1}\)
If a wheel turns with constant angular speed then
Each point on its rim moves with constant velocity
Each point on its rim moves with constant acceleration
The angle through which the wheel turns in each second decreases as time goes on
The wheel turns through equal angles in equal times
Ans: The wheel turns through equal angles in equal times
A boy suddenly comes and sit on the circular rotating table. What will remain conserved
Angular momentum
Linear velocity
Kinetic energy
None of these
Ans: Angular momentum
A wheel rotates about an axis passing through the center and perpendicular to the plane with slowly increasing angular speed. Then it has
Radial velocity and radial acceleration
Tangential velocity and radial acceleration
Tangential velocity and tangential acceleration
Tangential velocity but acceleration having both components
Ans: Tangential velocity but acceleration having both components
Ten seconds after an electric fan is turned on, the fan rotates at \(300rev/min\). Its average angular acceleration is
\(30 rad/s^2\)
\(3.14rad/s^2\)
\(30 rev/s^2\)
\(500 rev/s^2\)
Ans: \(3.14rad/s^2\)
At the surface of the earth, an object of mass \(m\) has weight \(w\). If this object is transported to an altitude that's twice the radius of the earth, then, at the new location,
Its mass is \(m/2\) and its weight is \(w/2\)
Its mass is \(m/2\) and its weight is \(w/4\)
Its mass is \(m\) and its weight is \(w/9\)
Its mass is \(m\) and its weight is \(w/4\)
Ans: Its mass is \(m\) and its weight is \(w/4\)
When a mass is rotated in a plane about a fixed point, its angular momentum is directed along
The radius
The tangent to the orbit
A line at an angle of \(45^o\) to the plane of rotation
The axis of rotation
Ans: The axis of rotation
When a body moves in a circle, the angle between its linear velocity and angular velocity is always
\(180^o\)
\(0^o\)
\(90^o\)
\(45^o\)
Ans: \(90^o\)
An arc of length equal to the circumference of circle subtends an angle
\(\pi\) radian
\(2\pi\) radian
\(\pi/2\) radian
\(4\pi\) radian
Ans: \(2\pi\) radian
A mass slides down on an inclined plane and reach the bottom with velocity \(v\). if the bottom would be same mass were in term of a ring which rolls down this plane, its linear speed at the bottom would be
\(v\)
\(\frac{v}{\sqrt{2}}\)
\(\sqrt{2}v\)
\(2v\)
Ans: \(\frac{v}{\sqrt{2}}\)
When a body is whirled in a horizontal circle by means of a string the centripetal force is supplied by
Mass of a body
Velocity of body
Tension in the string
Centripetal acceleration
Ans: Tension in the string
What remains constant when the earth revolve around the sun
Linear momentum
Linear K.E
Angular K.E
Angular momentum
Ans: Angular momentum
A satellite is currently orbiting Earth in a circular orbit of radius \(R\). its kinetic energy is \(K_1\). If the satellite is moved and enters a new circular orbit of radius \(2R\), what will be its kinetic energy?
\(\frac{K_1}{4}\)
\(\frac{K_1}{2}\)
\(K_1\)
\(2K_1\)
Ans: \(\frac{K_1}{2}\)
A stone is whirled in a vertical circle at the end of a string. When the stone is at the highest position the tension in the string is
Maximum
Zero
Equal to the weight of the stone
Less than the weight of the stone
Ans: Equal to the weight of the stone
The angular speed of hour's hand of mechanical watch is _______ radian per hours
\(\pi/6\)
\(\pi/4\)
\(\pi/12\)
\(\pi/8\)
Ans: \(\pi/6\)
\(\tau\) for an object rotating about a fixed axis, where \(\tau\) is the net torque acting on it, \(I\) is its rotational inertia, and \(\alpha\) is its angular acceleration. This expression:
Follows directly from Newton's second law
Is the definition of angular acceleration
Is the definition of rotational inertia
Is the definition of torque
Ans: Follows directly from Newton's second law
If a car moves with a uniform speed of \(2m/s\) in a circle of radius \(0.4m\). Its angular speed is
\(4 rad/s\)
\(5 rad/s\)
\(1.6 rad/s\)
\(2.8 m/s\)
Ans: \(5 rad/s\)
The mean distance from Saturn to the sun is \(9\) times greater than the mean distance from Earth to the sun. How long is a Saturn year?
\(18\) Earth years
\(27\) Earth years
\(81\) Earth years
\(243\) Earth years
Ans: \(27\) Earth years
A body moving along the circumference of a circle, complete two revolutions. If the radius of the circular path is \(R\), total angular displacement covered is
\(\pi R\)
\(2\pi R\)
Zero
\(4\pi\)
Ans: \(4\pi\)
A hoop rolls with Constant velocity and without sliding along level ground. Its rotational kinetic energy is:
Hall its translational kinetic energy
Twice its translational kinetic energy
Four times its translational kinetic energy
The same as its translational kinetic energy
Ans: The same as its translational kinetic energy
Time taken by geostationary satellite to complete one rotation around earth is
\(1\) year
\(1\) day
\(1\) hour
\(84\) min
Ans: \(1\) day
The direction of angular momentum is along
Tangent to the circle
Inward the radius
Axis of rotation
Outward of the radius
Ans: Axis of rotation
If a wheel of radius \(r\) turns through an angle of \(30^o\), then the distance through which any point on its rim moves is
\(\frac{\pi}{3}r\)
\(\frac{\pi}{6}r\)
\(\frac{\pi}{30}r\)
\(\frac{\pi}{180}r\)
Ans: \(\frac{\pi}{6}r\)
In angular motion, Newton's second law of motion is
\(F=ma\)
\(F=\Delta p/\Delta t\)
\(\tau=1\alpha\)
All of above
Ans: \(\tau=1\alpha\)
Angular speed of second's hand of a watch in \(rad/s\) is
\(\pi\)
\(\pi/2\)
\(\pi/30\)
\(\pi/180\)
Ans: \(\pi/30\)
The angle subtended by an arc equal to radius is
\(1 rad\)
\(1^o\)
\(1 rev\)
All
Ans: \(1 rad\)
What is outward force acting on a mass of \(10kg\) when rotating at one end of an inelastic string \(10m\) long at speed of \(1m/s\)?
\(1N\)
\(10N\)
\(2N\)
\(100N\)
Ans: \(1N\)
If we whirl a stone at the end of a string in the vertical circle, it is likely to break when the stone is
At the highest point
At the lowest point
At any point during motion
At the point where gravity is not acting
Ans: At the lowest point
Global positioning system consists of how many satellites?
\(24\) natural satellites
\(24\) artificial satellites
\(3\) synchronous satellites
Both b and c
Ans: \(24\) artificial satellites
A man of weight \(w\) is standing on an elevator which is ascending with an acceleration \(a\). The apparent weight of the man is

\(mg\)
\(ma-mg\)
\(mg+ma\)
\(mg-ma\)
Ans: \(mg+ma\)

Practice Exercise¶

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