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Q.1. Two objects of mass 10 kg and 20 kg respectively are connected to the two ends of a rigid rod of length 10 m with negligible mass. The distance of the center of mass of the system from the 10 kg mass is [2022]
(1) 20/3 m
(2) 10 m
(3) 5 m
(4) 10/3 m
Ans: (1)
Q.2. The ratio of the radius of gyration of a thin uniform disc about an axis passing through its center and normal to its plane to the radius of gyration of the disc about its diameter is
(1)√2: 1
(2) 4: 1
(3) 1: √2
(4) 2: 1 [2022]
Ans. (1)
Q.3. From a circular ring of mass 'M' and radius 'R' an arc corresponding to a 90° sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is 'K' times 'MR^{2}'. Then the value of 'K' is : [2021]
A: 1/4
B: 1/8
C: 3/4
D: 7/8
Ans: C
M_{remain} = 3/4M
I = M_{remain} R^{2}
= 3/4MR^{2}
Q.4. A uniform rod of length 200 cm and mass 500 g is balanced on a wedge placed at 40 cm mark. A mass of 2 kg is suspended from the rod at 20 cm and another unknown mass 'm' is suspended from the rod at 160 cm mark as shown in the figure. Find the value of 'm' such that the rod is in equilibrium. (g=10 m/s^{2}) [2021]
A: 1/6 kg
B: 1/12 kg
C: 1/2 kg
D: 1/3 kg
Ans: B
By balancing torque,
2g x 20 = 0.5g x 60 + mg x 120
m = 0.5 / 6 kg = 1/12 kg
Q.5. Find the torque about the origin when a force ofacts on a particle whose position vector is [2020]
A:
B:
C:
D:
Ans: A
Q.6. Two particles of mass 5kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1m with negligible mass. The centre of mass of the system from the 5kg particle is nearly at a distance of: [2020]
A: 67 cm
B: 80 cm
C: 33 cm
D: 50 cm
Ans: A
Q.7. A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after 2π revolutions is [2019]
A: 2 × 10^{6} N m
B: 2 × 10^{3} N m
C: 12 × 10^{4} N m
D: 2 × 10^{6} N m
Ans: A
Solution: Work energy theorem.
θ = 2π revolution
= 2π × 2π = 4π^{2} rad
Q.8. Two particles A and B are moving in uniform circular motion in concentric circles of radii r_{A} and r_{B} with speed v_{A} and v_{B} respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be: [2019]
A: r_{A} : r_{B}
B: v_{A} : v_{B}
C: r_{B} : r_{A}
D: 1 : 1
Ans: D
Solution:
Q.9. Three objects, A : (a solid sphere), B : (a thin circular disk) and C = (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed ω about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation: [2018]
A: W_{C} > W_{B} > W_{A}
B: W_{A} > W_{B} > W_{C}
C: W_{B} > W_{A} > W_{C}
D: W_{B} > W_{A} > W_{C}
Ans: A
Solution:
Q.10. The moment of the force, at (2, 0, –3), about the point (2, –2, –2), is given by: [2018]
A:
B:
C:
D:
Ans: D
Solution:
Q.11. A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy (Kr) simultaneously. The ratio Kt : (Kt + Kr) for the sphere is [2018]
A: 7 : 10
B: 5 : 7
C: 10 : 7
D: 2 : 5
Ans: B
Solution:
Q.12. A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere ? [2018]
A: Angular velocity
B: Moment of inertia
C: Rotational kinetic energy
D: Angular momentum
Ans: D
Solution:
Q.13. A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N ? [2017]
A: 0.25 rad/s^{2}
B: 25 rad/s^{2}
C: 5 m/s^{2}
D: 25 m/s^{2}
Ans: B
Solution:
Q.14. Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ω_{1} and ω_{2}. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is: [2017]
A:
B:
C:
D:
Ans: A
Solution:
Q.15. Which of the following statements are correct ? [2017]
(a) Centre of mass of a body always coincides with the centre of gravity of the body
(b) Central of mass of a body is the point at which the total gravitational torque on the body is zero
(c) A couple on a body produces both translational and rotation motion in a body
(d) Mechanical advantage greater than one means that small effort can be used to lift a large load
A: (a) and (b)
B: (b) and (c)
C: (c) and (d)
D: (b) and (d)
Ans: D
Solution: Centre of mass may lie on centre of gravity net torque of gravitational pull is zero about centre of mass.
Q.16. From a disc of radius R and mass M_{1} a circular hole of diameter R_{1} whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about at perpendicular axis, passing through the centre ? [2016]
A: 9MR^{2}/32
B: 15MR^{2}/32
C: 13MR^{2}/32
D: 11 MR^{2}/32
Ans: C
Solution:
Option C is correct Answer.
Q.17. A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first ? [2016]
A: Depends on their masses
B: Disk
C: Sphere
D: both reach at the same time
Ans: C
Solution: Time does not depend on mass, else
K^{2}/R^{2} is least for sphere and hence least time is taken by sphere
Q.18. A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of 2.0 rad s^{2}. Its net acceleration in ms^{2} at the end of 2.0 s is approximately : [2016]
A: 3.0
B: 8.0
C: 7.0
D: 6.0
Ans: B
Solution: The angular speed of disc increases with time, and hence centripetal acceleration also increases.
Q.19. Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX' which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about XX' axis is : [2015]
A: 4 mr^{2}
B: 11/5 mr^{2}
C: 3 mr^{2}
D: 16/5 mr^{2}
Ans: A
Solution:
Similarly the moment of inertia of the spherical shell C about the XX' axis is
Q.20. A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s^{−2} is: [2014]
A: 78.5 N
B: 157 N
C: 25 πN
D: 50 N
Ans: A
Solution:
Q.21. The ratio of the accelerations for a solid sphere (mass ‘m’ and radius ‘R’) rolling down an incline of angle ‘θ’ without slipping and slipping down the incline without rolling is : [2014]
A: 2 : 5
B: 7 : 5
C: 5 : 7
D: 2 :3
Ans: C
Solution:
Q.22. A body of mass (4m) is lying in x−y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass (m) move perpendicular to each other with equal speeds (ν). The total kinetic energy generated due to explosion is : [2014]
A: 2 mν^{2}
B: 4 mν^{2}
C: mν^{2}
D: 3/2 mν^{2}
Ans: D
Solution:
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