# A rod $$\mathrm{PQ}$$ of mass $$M$$ and length $$L$$ is hinged at end $$\mathrm{P}$$. The rod is kept horizontal by a massless string tied to point $$\mathrm{Q}$$ as shown in the figure. When the string is cut, the initial angular acceleration of the rod is:               1. $$\frac{g}{L}$$ 2. $$\frac{2g}{L}$$ 3. $$\frac{2g}{3L}$$ 4. $$\frac{3g}{2L}$$

Subtopic:  Torque |
80%
From NCERT
AIPMT - 2013
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along:

 1 a line perpendicular to the plane of rotation 2 the line making an angle of $$45^{\circ}$$ to the plane of rotation 3 the radius 4 the tangent to the orbit

Subtopic:  Angular Momentum |
75%
From NCERT
AIPMT - 2012
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

Two persons of masses $$55$$ kg and $$65$$ kg respectively, are at the opposite ends of a boat. The length of the boat is $$3.0$$ m and weighs $$100$$ kg. The $$55$$ kg man walks up to the $$65$$ kg man and sits with him. If the boat is in still water, the centre of mass of the system shifts by:
1. $$3.0$$ m
2. $$2.3$$ m
3. zero
4. $$0.75$$ m

Subtopic:  Center of Mass |
76%
From NCERT
AIPMT - 2012
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

$$\mathrm{ABC}$$ is an equilateral triangle with $$O$$ as its centre. $$F_1$$, $$F_2$$, and $$F_3$$ represent three forces acting along the sides $$\mathrm{AB},$$ $$\mathrm{BC}$$ and $$\mathrm{AC}$$ respectively. If the total torque about $$O$$ is zero, then the magnitude of $$F_3$$ is:

1. $$F_1+F_2$$
2. $$F_1-F_2$$
3. $$\frac{F_1+F_2}{2}$$
4. $$2F_1+F_2$$

Subtopic:  Torque |
76%
From NCERT
AIPMT - 2012
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

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 |
76%
From NCERT
AIPMT - 2011
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

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 $$I_0$$. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is:
1. $$I_0+\frac{ML^2}{4}$$
2. $$I_0+2ML^2$$
3. $$I_0+ML^2$$
4. $$I_0+\frac{ML^2}{2}$$

Subtopic:  Moment of Inertia |
80%
From NCERT
AIPMT - 2011
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

A circular disk of a moment of inertia $$\mathrm{I_t}$$ is rotating in a horizontal plane, about its symmetric axis, with a constant angular speed $$\omega_i.$$ Another disk of a moment of inertia $$\mathrm{I_b}$$ 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 $$\omega_f.$$ The energy lost by the initially rotating disc due to friction is:
1. $$\frac{1}{2} \frac{\mathrm{I}_{\mathrm{b}}^2}{\left(\mathrm{I}_{\mathrm{t}}+\mathrm{I}_{\mathrm{b}}\right)} \omega_{\mathrm{i}}^2$$

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

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

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

Subtopic:  Angular Momentum |
72%
From NCERT
AIPMT - 2010
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

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 |
78%
From NCERT
AIPMT - 2010
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

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 |
78%
From NCERT
AIPMT - 2010
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

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 |
82%
From NCERT
AIPMT - 2009
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints