General
✓✗A horizontal turntable of moment of inertia 2 kg m2 rotates freely at 6 rad/s. A small 0.5 kg lump of clay is dropped onto it at 2 m from the axis and sticks. The new angular speed is
- 2 rad/s
- 6 rad/s
- 4 rad/s
- 3 rad/s
General
✓✗Three rings, each of mass m and radius r, lie in one plane touching one another, their centres forming an equilateral triangle. The moment of inertia of the system about an axis through the centre of one ring perpendicular to the plane is
- 11mr2
- 9mr2
- 3mr2
- 7mr2
General
✓✗The centre of mass of a system of two particles is nearer to
- the lighter particle
- the faster particle
- neither; it is always at the midpoint
- the heavier particle
General
✓✗A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has a speed of 20 cm/s. How much work is needed to stop it?
- 1 J
- 2 J
- 3 J
- 30 kJ
General
✓✗A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If the radius of the ball is R, the fraction of the total energy associated with its rotational energy will be
- \( \dfrac{K^2}{K^2 + R^2} \)
- \( \dfrac{K^2 + R^2}{R^2} \)
- \( \dfrac{K^2}{R^2} \)
- \( \dfrac{R^2}{K^2 + R^2} \)
General
✓✗A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q. When the string is cut, the initial angular acceleration of the rod is
- \( \dfrac{3g}{2L} \)
- \( \dfrac{2g}{3L} \)
- \( \dfrac gL \)
- \( \dfrac{2g}{L} \)
General
✓✗Assertion: When a person on a freely rotating stool pulls in two dumbbells, the rotational kinetic energy of the system increases.
Reason: The angular momentum of the system remains constant while its moment of inertia decreases.
Reason: The angular momentum of the system remains constant while its moment of inertia decreases.
- Both Assertion and Reason are true and Reason is the correct explanation of Assertion
- Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
- Assertion is true but Reason is false
- Both Assertion and Reason are false
General
✓✗A uniform metre rule is balanced at its 50 cm mark. A 20 g mass is hung at the 30 cm mark. To balance it, a 40 g mass must be hung at
- the 40 cm mark
- the 80 cm mark
- the 70 cm mark
- the 60 cm mark
General
✓✗The centre of mass of a uniform triangular lamina lies at
- one of its vertices
- the point of intersection of its altitudes
- the midpoint of its longest side
- the point of intersection of its medians (centroid)
General
✓✗The work needed to increase the angular speed of a wheel of moment of inertia 2 kg m2 from 10 rad/s to 20 rad/s is
- 200 J
- 300 J
- 400 J
- 100 J
General
✓✗Two equal and opposite forces whose lines of action are different constitute
- a third-law pair
- a central force
- an equilibrium pair
- a couple
General
✓✗A particle of mass 1 kg is projected with speed 20 m s−1 at 45° to the horizontal. The magnitude of its angular momentum about the point of projection just before it lands is (g = 10 m s−2)
- \( 400\sqrt2 \) kg m2 s−1
- \( 200\sqrt2 \) kg m2 s−1
- 400 kg m2 s−1
- 800 kg m2 s−1
General
✓✗A diver performing somersaults tucks his body in. This
- increases his angular momentum
- reduces his angular momentum
- increases his moment of inertia
- reduces his moment of inertia and increases his angular velocity
General
✓✗For a lever, mechanical advantage is defined as
- effort arm × load arm
- effort divided by load
- load divided by effort
- load × effort
General
✓✗A particle of mass 1 kg has position \( \vec r = (t\,\hat i + t^2\,\hat j) \) m. Its angular momentum about the origin at t = 1 s is
- \( \hat k \) kg m2 s−1
- \( 3\hat k \) kg m2 s−1
- \( -\hat k \) kg m2 s−1
- \( 2\hat k \) kg m2 s−1