A body of mass 100 grams is tied to one end of a string and revolved along a circular path in the horizontal plane. The radius of the circle is $50 \mathrm{~cm}$. If the body revolves with a constant angular speed of $20 \mathrm{rad} / \mathrm{s}$, find the
1. period of revolution
2. linear speed
3. centripetal acceleration of the body.
1. period of revolution
2. linear speed
3. centripetal acceleration of the body.
Q 30.2
Download our app for free and get started
Data : $m=100 \mathrm{~g}=0.1 \mathrm{~kg}, \mathrm{r}=50 \mathrm{~cm}=0.5 \mathrm{~m}, \omega=20 \mathrm{rad} / \mathrm{s}$
1. The period of revolution of the body,
$
T=\frac{2 \pi}{\omega}=\frac{2 \times 3.142}{20}=0.3142 \mathrm{~s}
$
2. Linear speed, $v=\omega r=20 \times 0.5=10 \mathrm{~m} / \mathrm{s}$
3. Centripetal acceleration,
$
a_c=w^2 r=(20)^2 \times 0.5=200 \mathrm{~m} / \mathrm{s}^2
$
1. The period of revolution of the body,
$
T=\frac{2 \pi}{\omega}=\frac{2 \times 3.142}{20}=0.3142 \mathrm{~s}
$
2. Linear speed, $v=\omega r=20 \times 0.5=10 \mathrm{~m} / \mathrm{s}$
3. Centripetal acceleration,
$
a_c=w^2 r=(20)^2 \times 0.5=200 \mathrm{~m} / \mathrm{s}^2
$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A boy standing at the centre of a turntable with his arms outstretched is set into rotation with angular speed $\omega \mathrm{rev} / \mathrm{min}$. When the boy folds his arms back, his moment of inertia reduces to $\frac{2}{5}$ th its initial value. Find the ratio of his final kinetic energy of rotation to his initial kinetic energy.View Solution
- 2View SolutionState the MI of a thin rectangular plate-of mass M, length l and breadth b- about an axis passing through its centre and parallel to its length. Hence find its MI about a parallel axis along one edge.
- 3View SolutionWhat is vertical circular motion? Comment on its two types.
- 4A ballet dancer spins about a vertical axis at $2.5 \pi \mathrm{rad} / \mathrm{s}$ with his arms outstretched. With the arms folded, the MI about the same axis of rotation changes by $25 \%$. Calculate the new speed of rotation in rpm.View Solution
- 5View SolutionA loop-the-loop cart runs down an incline into a vertical circular track of radius 3 m and then describes a complete circle. Find the minimum height above the top of the circular track from which the cart must be released.
- 6A stone of mass $1 \mathrm{~kg}$, attached at the end of a $1 \mathrm{~m}$ long string, is whirled in a horizontal circle. If the string makes an angle of $30^{\circ}$ with the vertical, calculate the centripetal force acting on the stone.View Solution
- 7View SolutionWhy do grinding wheels have large mass and moderate diameter?
- 8View SolutionWhat is the recommendations on loading a vehicle for not toppling easily?
- 9A circular race course track has a radius of $500 \mathrm{~m}$ and is banked at $10^{\circ}$. The coefficient of static friction between the tyres of a vehicle and the road surface is 0.25 . ComputeView Solution
(i) the maximum speed to avoid slipping
(ii) the optimum speed to avoid wear and tear of the tyres. - 10View SolutionState the MI of a thin rectangular plate-of mass M, length l and breadth b about its transverse axis passing through its centre. Hence find its MI about a parallel axis through the midpoint of edge of length b.