Work, Energy & Power in Case of Rotation of a Rigid Body about Fixed Axis
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366268 As shown in the figure, a bob of mass m is tied by massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from rest the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be
supporting img

1 \(r \sqrt{\dfrac{3}{2 g h}}\)
2 \(\dfrac{1}{r} \sqrt{\dfrac{4 g h}{3}}\)
3 \(r \sqrt{\dfrac{3}{4 g h}}\)
4 \(\dfrac{1}{r} \sqrt{\dfrac{2 g h}{3}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366269 The moment of inertia of a body about a given axis is \(1.2\;kg - {m^2}\). Initially, the body is at rest. In order to produce a rotational kinetic energy of \(1500\;J\), and angular acceleration of \(25\,rad{s^{ - 2}}\) must be applied about that axis for a duration of

1 \(10\;s\)
2 \(4\;s\)
3 \(8\;s\)
4 \(2\;s\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366270 A force of \(15\;N\) is applied on a cord wrapped around a cylinder of mass \(2\;kg.\) The cylinder rolls without slipping on the floor. What is its kinetic energy (in joule) when cylinder has moved by a distance of \(3{\rm{/}}5m\)?
supporting img

1 \(2\,J\)
2 \(5\,J\)
3 \(9\,J\)
4 \(15\,J\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366271 Which of these statements(s) is/are incorrect?
I.
Moment of force is a vector quantity.
II.
Angular momentum is a vector quantity.
III.
Angular momentum of a particle moving in a straight line is always constant with respect to fixed point.
IV.
\(K . E_{\text {rot }}=L \omega\)

1 Only I
2 Only II
3 Only III
4 Only IV
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366268 As shown in the figure, a bob of mass m is tied by massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from rest the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be
supporting img

1 \(r \sqrt{\dfrac{3}{2 g h}}\)
2 \(\dfrac{1}{r} \sqrt{\dfrac{4 g h}{3}}\)
3 \(r \sqrt{\dfrac{3}{4 g h}}\)
4 \(\dfrac{1}{r} \sqrt{\dfrac{2 g h}{3}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366269 The moment of inertia of a body about a given axis is \(1.2\;kg - {m^2}\). Initially, the body is at rest. In order to produce a rotational kinetic energy of \(1500\;J\), and angular acceleration of \(25\,rad{s^{ - 2}}\) must be applied about that axis for a duration of

1 \(10\;s\)
2 \(4\;s\)
3 \(8\;s\)
4 \(2\;s\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366270 A force of \(15\;N\) is applied on a cord wrapped around a cylinder of mass \(2\;kg.\) The cylinder rolls without slipping on the floor. What is its kinetic energy (in joule) when cylinder has moved by a distance of \(3{\rm{/}}5m\)?
supporting img

1 \(2\,J\)
2 \(5\,J\)
3 \(9\,J\)
4 \(15\,J\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366271 Which of these statements(s) is/are incorrect?
I.
Moment of force is a vector quantity.
II.
Angular momentum is a vector quantity.
III.
Angular momentum of a particle moving in a straight line is always constant with respect to fixed point.
IV.
\(K . E_{\text {rot }}=L \omega\)

1 Only I
2 Only II
3 Only III
4 Only IV
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366268 As shown in the figure, a bob of mass m is tied by massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from rest the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be
supporting img

1 \(r \sqrt{\dfrac{3}{2 g h}}\)
2 \(\dfrac{1}{r} \sqrt{\dfrac{4 g h}{3}}\)
3 \(r \sqrt{\dfrac{3}{4 g h}}\)
4 \(\dfrac{1}{r} \sqrt{\dfrac{2 g h}{3}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366269 The moment of inertia of a body about a given axis is \(1.2\;kg - {m^2}\). Initially, the body is at rest. In order to produce a rotational kinetic energy of \(1500\;J\), and angular acceleration of \(25\,rad{s^{ - 2}}\) must be applied about that axis for a duration of

1 \(10\;s\)
2 \(4\;s\)
3 \(8\;s\)
4 \(2\;s\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366270 A force of \(15\;N\) is applied on a cord wrapped around a cylinder of mass \(2\;kg.\) The cylinder rolls without slipping on the floor. What is its kinetic energy (in joule) when cylinder has moved by a distance of \(3{\rm{/}}5m\)?
supporting img

1 \(2\,J\)
2 \(5\,J\)
3 \(9\,J\)
4 \(15\,J\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366271 Which of these statements(s) is/are incorrect?
I.
Moment of force is a vector quantity.
II.
Angular momentum is a vector quantity.
III.
Angular momentum of a particle moving in a straight line is always constant with respect to fixed point.
IV.
\(K . E_{\text {rot }}=L \omega\)

1 Only I
2 Only II
3 Only III
4 Only IV
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366268 As shown in the figure, a bob of mass m is tied by massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from rest the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be
supporting img

1 \(r \sqrt{\dfrac{3}{2 g h}}\)
2 \(\dfrac{1}{r} \sqrt{\dfrac{4 g h}{3}}\)
3 \(r \sqrt{\dfrac{3}{4 g h}}\)
4 \(\dfrac{1}{r} \sqrt{\dfrac{2 g h}{3}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366269 The moment of inertia of a body about a given axis is \(1.2\;kg - {m^2}\). Initially, the body is at rest. In order to produce a rotational kinetic energy of \(1500\;J\), and angular acceleration of \(25\,rad{s^{ - 2}}\) must be applied about that axis for a duration of

1 \(10\;s\)
2 \(4\;s\)
3 \(8\;s\)
4 \(2\;s\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366270 A force of \(15\;N\) is applied on a cord wrapped around a cylinder of mass \(2\;kg.\) The cylinder rolls without slipping on the floor. What is its kinetic energy (in joule) when cylinder has moved by a distance of \(3{\rm{/}}5m\)?
supporting img

1 \(2\,J\)
2 \(5\,J\)
3 \(9\,J\)
4 \(15\,J\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366271 Which of these statements(s) is/are incorrect?
I.
Moment of force is a vector quantity.
II.
Angular momentum is a vector quantity.
III.
Angular momentum of a particle moving in a straight line is always constant with respect to fixed point.
IV.
\(K . E_{\text {rot }}=L \omega\)

1 Only I
2 Only II
3 Only III
4 Only IV