An object flying in the air with velocity \((20 \hat{i}+25 \hat{j}-12 \hat{k})\) suddenly breaks into two pieces whose masses are in the ratio of \(1:5.\) The smaller mass flies off with a velocity \((100 \hat{i}+35 \hat{j}+8 \hat{k})\). The velocity of the larger piece will be:
1. \( 4 \hat{i}+23 \hat{j}-16 \hat{k}\)
2. \( -100 \hat{i}-35 \hat{j}-8 \hat{k} \)
3. \( 20 \hat{i}+15 \hat{j}-80 \hat{k} \)
4. \( -20 \hat{i}-15 \hat{j}-80 \hat{k}\)

Subtopic:  Linear Momentum |
 74%
From NCERT
NEET - 2019
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A particle starting from rest moves in a circle of radius \(r\). It attains a velocity of \(v_0~\text{m/s}\) on completion of \(n\) rounds. Its angular acceleration will be:

1. \( \frac{v_0}{n} ~\text{rad} / \text{s}^2\) 2. \( \frac{v_0^2}{2 \pi {nr}^2}~ \text{rad} / \text{s}^2 \)
3. \( \frac{v_o^2}{4 \pi {n}{r}^2}~ \text{rad} / \text{s}^2 \) 4. \( \frac{v_0^2}{4 \pi {nr}} ~\text{rad} / \text{s}^2 \)

Subtopic:  Rotational Motion: Kinematics |
 51%
From NCERT
NEET - 2019
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A particle of mass \(5m\) at rest suddenly breaks on its own into three fragments. Two fragments of mass \(m\) each move along mutually perpendicular directions with speed \(v\) each. The energy released during the process is:
1. \(\frac{3}{5}mv^2\)
2. \(\frac{5}{3}mv^2\)
3. \(\frac{3}{3}mv^2\)
4. \(\frac{4}{3}mv^2\)

Subtopic:  Linear Momentum |
 58%
From NCERT
NEET - 2019
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A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle of inclination 30°. The centre of mass of the cylinder has a speed of 4 m/s. The distance travelled by the cylinder on the inclined surface will be [take g= 10 m/s2] :

1. 2.2 m

2. 1.6 m

3. 1.2 m

4. 2.4 m

Subtopic:  Rolling Motion (OLD NCERT) |
 52%
From NCERT
NEET - 2019
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Two balls of mass M = 9 g and m = 3 g are attached by massless threads AO and OB. The length AB is 1 m. They are set in rotational motion in a horizontal plane about a vertical axis at O with constant angular velocity ω. The ratio of length OB  and AO OBAO for which the tension in threads are same will be-

(1) 1

(2) 2

(3) 3

(4) 4

Subtopic:  Rotational Motion: Kinematics |
 70%
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Internal forces cannot change:

(1)  the kinetic energy of a system.

(2)  the mechanical energy of a system.

(3)  the momentum of a system.

(4)  all of these

Subtopic:  Linear Momentum |
 56%
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The masses m1 and m2 with m1 < m2 are connected to the two ends of a compressed spring. Now, when the masses are released on a smooth surface, they will move away with

(1)  the same magnitude of the force.

(2)  the equal magnitude of linear momentum.

(3)  the greater kinetic energy of the first body than that of the second body.

(4)  All of these

Subtopic:  Linear Momentum |
 70%
From NCERT
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Four masses are joined to light circular frames as shown in the figure. The radius of gyration of this system about an axis passing through the center of the circular frame and perpendicular to its plane would be: (where 'a' is the radius of the circle)
                   
1.  a2

2.  a2

3.  a

4.  2a

Subtopic:  Moment of Inertia |
 64%
From NCERT
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A disc of mass \(M\) and radius \(R\) starts falling down as shown in the figure. The string unwinds without slipping on the disc. The instantaneous power developed by the tension is:

     
1. \((T\times R \omega)\)
2. \((T\times R \omega)/2\)
3. \(2(T\times R \omega)\)
4. zero

Subtopic:  Rolling Motion (OLD NCERT) |
From NCERT
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The rotational analouge of equation \(F=\frac{mdv}{dt}\) is:

1. \(\tau=\frac{dL}{dt}\)
2. \(\tau=I \frac{d\omega}{dt}\)
3. \(\tau=I \frac{dI}{dt}\omega\)
4. \(\tau=I\frac{d\omega}{dt}+\frac{dI}{dt}\omega\)
Subtopic:  Rotational Motion: Kinematics |
 77%
From NCERT
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