What is the value of linear velocity if $$\overset{\rightarrow}{\omega} = 3\hat{i} - 4\hat{j} + \hat{k}$$ and $$\overset{\rightarrow}{r} = 5\hat{i} - 6\hat{j} + 6\hat{k}$$  :

 1 $$6 \hat{i}+2 \hat{j}-3 \hat{k}$$ 2 $$-18 \hat{i}-13 \hat{j}+2 \hat{k}$$ 3 $$4 \hat{i}-13 \hat{j}+6 \hat{k}$$ 4 $$6 \hat{i}-2 \hat{j}+8 \hat{k}$$
Subtopic:  Circular Motion |
85%
From NCERT
PMT - 2000
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The angle turned by a body undergoing circular motion depends on the time as given by the equation, $\theta ={\theta }_{0}+{\theta }_{1}t+{\theta }_{2}{t}^{2}$. It can be deduced that the angular acceleration of the body is?

1. θ1

2. θ2

3. 2θ1

4. 2θ2

Subtopic:  Circular Motion |
84%
From NCERT
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If the equation for the displacement of a particle moving on a circular path is given by $$\theta = 2t^3 + 0.5$$ where θ is in radians and t in seconds, then the angular velocity of the particle after 2 sec from its start is:

Subtopic:  Circular Motion |
81%
From NCERT
AIIMS - 1998
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A particle moves in a circle of radius $$5$$ cm with constant speed and time period $$0.2\pi$$ s. The acceleration of the particle is:

 1 $$25$$ m/s2 2 $$36$$ m/s2 3 $$5$$ m/s2 4 $$15$$ m/s2
Subtopic:  Circular Motion |
80%
From NCERT
AIPMT - 2011
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A car moves on a circular path such that its speed is given by v = Kt, where K =constant and t is time. Also given: radius of the circular path is r. The net acceleration of the car at time t will be:

1.

2. 2K

3. K

4.

Subtopic:  Circular Motion |
80%
From NCERT
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Two particles A and B are moving in a uniform circular motion in concentric circles of radii $$r_A$$ and $$r_B$$ with speeds $$v_A$$ and $$v_B$$ respectively. Their time periods of rotation are the same. The ratio of the angular speed of $$A$$  to that of $$B$$ will be:

 1 $$1: 1$$ 2 $$r_A: r_B$$ 3 $$v_A: v_B$$ 4 $$r_B: r_A$$
Subtopic:  Circular Motion |
79%
From NCERT
NEET - 2019
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The position vector of a particle is $\stackrel{\to }{\mathrm{r}}$ $=$ $\left(\mathrm{a}\right)$ $\mathrm{sin}$ $\mathrm{\omega t}\stackrel{^}{\mathrm{i}}$ $+$ $\left(\mathrm{a}\right)$ $\mathrm{cos}$ $\mathrm{\omega t}\stackrel{^}{\mathrm{j}}$. The velocity of the particle is:

 1 parallel to the position vector. 2 at 60° with position vector. 3 parallel to the acceleration vector. 4 perpendicular to the position vector.

Subtopic:  Circular Motion |
79%
From NCERT
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A particle is moving along a circle of radius $$R$$ with constant speed $$\mathrm{v}_0$$. What is the magnitude of change in velocity when the particle goes from point $$A$$ to $$B$$ as shown?

 1 $$2 \mathrm{v}_0 \sin \frac{\theta}{2}$$ 1 $$\mathrm{v}_0 \sin \frac{\theta}{2}$$ 3 $$2 \mathrm{v}_0 \cos \frac{\theta}{2}$$ 4 $$\mathrm{v}_0 \cos \frac{\theta}{2}$$
Subtopic:  Circular Motion |
77%
From NCERT
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If a particle is moving in a circular orbit with constant speed, then:

 1 its velocity is variable. 2 its acceleration is variable. 3 its angular momentum is constant. 4 All of the above

Subtopic:  Circular Motion |
78%
From NCERT
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A stone tied to the end of a 1 m long string is whirled in a horizontal circle at a constant speed. If the stone makes 22 revolutions in 44 seconds, what is the magnitude and direction of acceleration of the stone?

 1 $$\pi^2 \mathrm{~ms}^{-2}$$ and direction along the tangent to the circle. 2 $$\pi^2 \mathrm{~ms}^{-2}$$  and direction along the radius towards the centre. 3 $$\frac{\pi^2}{4} \mathrm{~ms}^{-2}$$ and direction along the radius towards the centre. 4 $$\pi^2 \mathrm{~ms}^{-2}$$ and direction along the radius away from the centre.

Subtopic:  Circular Motion |
76%
From NCERT
AIPMT - 2005
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