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

 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 |
86%
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. $$\theta_1$$
2. $$\theta_2$$
3. $$2\theta_1$$
4. $$2\theta_2$$

Subtopic:  Circular Motion |
84%
From NCERT
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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. $$\sqrt{K^{2} +\left(\frac{K^{2} t^{2}}{r}\right)^{2}}$$
2. $$2K$$
3. $$K$$
4. $$\sqrt{K^{2} + K^{2} t^{2}}$$

Subtopic:  Circular Motion |
80%
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 $$\pi^2 ~\text{ms}^{-2}$$ and direction along the tangent to the circle. 2 $$\pi^2 ~\text{ms}^{-2}$$  and direction along the radius towards the centre. 3 $$\frac{\pi^2}{4}~\text{ms}^{-2}$$ and direction along the radius towards the centre. 4 $$\pi^2~\text{ms}^{-2}$$ and direction along the radius away from the centre.

Subtopic:  Circular Motion |
77%
From NCERT
AIPMT - 2005
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The position vector of a particle is $$\vec{r}= a \sin\omega t \hat{i} + a\cos \omega t \hat{j}$$. The velocity of the particle is:
 1 parallel to the position vector. 2 at $$60^{\circ}$$ with position vector. 3 parallel to the acceleration vector. 4 perpendicular to the position vector.
Subtopic:  Circular Motion |
80%
From NCERT
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A car is moving at a speed of $$40$$ m/s on a circular track of radius $$400$$ m. This speed is increasing at the rate of $$3$$ m/s2. The acceleration of the car is:
1. $$4$$ m/s2
2. $$7$$ m/s2
3. $$5$$ m/s2
4. $$3$$ m/s2

Subtopic:  Circular Motion |
75%
From NCERT
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Certain neutron stars are believed to be rotating at about $$1$$ rev/s. If such a star has a radius of $$20$$ km, the acceleration of an object on the equator of the star will be:

 1 $$20 \times 10^8 ~\text{m/s}^2$$ 2 $$8 \times 10^5 ~\text{m/s}^2$$ 3 $$120 \times 10^5 ~\text{m/s}^2$$ 4 $$4 \times 10^8 ~\text{m/s}^2$$
Subtopic:  Circular Motion |
70%
From NCERT
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A particle moves with constant speed $$v$$ along a circular path of radius $$r$$ and completes the circle in time $$T$$. The acceleration of the particle is:
1. $$2\pi v / T$$
2. $$2\pi r / T$$
3. $$2\pi r^2 / T$$
4. $$2\pi v^2 / T$$

Subtopic:  Circular Motion |
62%
From NCERT
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