A solid cylinder of mass 3 kg is rolling on a horizontal surface with a velocity of 4 ms-1. It collides with a horizontal spring of force constant 200 Nm-1. The maximum compression produced in the spring will be: 1. 0.5 m 2. 0.6 m 3. 0.7 m 4. 0.2 m

Subtopic:  Rolling Motion |
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ABC is an equilateral triangle with O as its centre. F1, F2, and F3 represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero, then the magnitude of F3 is:

1. ${\mathrm{F}}_{1}+{\mathrm{F}}_{2}$

2. ${\mathrm{F}}_{1}-{\mathrm{F}}_{2}$

3. $\frac{{\mathrm{F}}_{1}+{\mathrm{F}}_{2}}{2}$

4. $2\left(\mathrm{F}+{\mathrm{F}}_{2}\right)$

Subtopic:  Torque |
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The instantaneous angular position of a point on a rotating wheel is given by the equation,
$$\theta(t)=2t^{3}-6t^{2}$$
The torque on the wheel becomes zero at:
1. $$t=0.5$$ s
2. $$t=0.25$$ s
3. $$t=2$$ s
4. $$t=1$$ s
Subtopic:  Rotational Motion: Kinematics |
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The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its mid-point and perpendicular to its length is I0. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is:

1.  ${\mathrm{I}}_{0}+{\mathrm{ML}}^{2}/4$

2.  ${\mathrm{I}}_{0}+2{\mathrm{ML}}^{2}$

3.  ${\mathrm{I}}_{0}+{\mathrm{ML}}^{2}$

4.  ${\mathrm{I}}_{0}+{\mathrm{ML}}^{2}/2$

Subtopic:  Moment of Inertia |
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A circular disk of a moment of inertia It is rotating in a horizontal plane, about its symmetric axis, with a constant angular speed ${\mathrm{\omega }}_{\mathrm{i}}$. Another disk of a moment of inertia Ib is dropped coaxially onto the rotating disk. Initially, the second disk has zero angular speed. Eventually, both the disks rotate with a constant angular speed ${\mathrm{\omega }}_{\mathrm{f}}$. The energy lost by the initially rotating disc due to friction is:

1. $\frac{1}{2}\frac{{\mathrm{I}}_{\mathrm{b}}^{2}}{\left({\mathrm{I}}_{\mathrm{t}}+{\mathrm{I}}_{\mathrm{b}}\right)}{\mathrm{\omega }}_{\mathrm{i}}^{2}$

2. $\frac{1}{2}\frac{{\mathrm{I}}_{\mathrm{t}}^{2}}{\left({\mathrm{I}}_{\mathrm{t}}+{\mathrm{I}}_{\mathrm{b}}\right)}{\mathrm{\omega }}_{\mathrm{i}}^{2}$

3. $\frac{1}{2}\frac{{\mathrm{I}}_{\mathrm{b}}-{\mathrm{I}}_{\mathrm{t}}}{\left({\mathrm{I}}_{\mathrm{t}}+{\mathrm{I}}_{\mathrm{b}}\right)}{\mathrm{\omega }}_{\mathrm{i}}^{2}$

4. $\frac{1}{2}\frac{{\mathrm{I}}_{\mathrm{b}}{\mathrm{I}}_{\mathrm{t}}}{\left({\mathrm{I}}_{\mathrm{t}}+{\mathrm{I}}_{\mathrm{b}}\right)}{\mathrm{\omega }}_{\mathrm{i}}^{2}$

Subtopic:  Angular Momentum |
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Two particles that are initially at rest, move towards each other under the action of their mutual attraction. If their speeds are v and 2v at any instant, then the speed of the centre of mass of the system will be:

1. 2v

2. 0

3. 1.5v

4. v

Subtopic:  Center of Mass |
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A man of 50 kg mass is standing in a gravity-free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed of 2 ms-1. When the stone reaches the floor, the distance of the man above the floor will be:

1. 9.9 m
2. 10.1 m
3. 10 m
4. 20 m

Subtopic:  Center of Mass |
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If $$\vec F$$ is the force acting on a particle having position vector $$\vec r$$ and $$\vec \tau$$ be the torque of this force about the origin, then:

 1 $$\vec r\cdot\vec \tau\neq0\text{ and }\vec F\cdot\vec \tau=0$$ 2 $$\vec r\cdot\vec \tau>0\text{ and }\vec F\cdot\vec \tau<0$$ 3 $$\vec r\cdot\vec \tau=0\text{ and }\vec F\cdot\vec \tau=0$$ 4 $$\vec r\cdot\vec \tau=0\text{ and }\vec F\cdot\vec \tau\neq0$$
Subtopic:  Torque |
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A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω. If two objects each of mass m are attached gently to the opposite ends of the diameter of the ring, the ring will then rotate with an angular velocity:

1. $\frac{\omega \left(M-2m\right)}{M+2m}$

2. $\frac{\omega M}{M+2m}$

3. $\frac{\omega \left(M+2m\right)}{M}$

4. $\frac{\omega M}{M+m}$

Subtopic:  Angular Momentum |
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Two bodies of mass 1 kg and 3 kg have position vectors  respectively. The centre of mass of this system has a position vector:
1. -2$\stackrel{^}{i}$+2$\stackrel{^}{k}$
2. -2$\stackrel{^}{i}$-$\stackrel{^}{j}$+$\stackrel{^}{k}$
3. 2$\stackrel{^}{i}$- $\stackrel{^}{j}$- 2$\stackrel{^}{k}$
4. -$\stackrel{^}{i}$+$\stackrel{^}{j}$+$\stackrel{^}{k}$

Subtopic:  Center of Mass |
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