Advertisements
Advertisements
Question
A particle is kept fixed on a turntable rotating uniformly. As seen from the ground the particle goes in a circle, its speed is 20 cm/s and acceleration is 20 cm/s2. The particle is now shifted to a new position to make the radius half of the original value. The new value of the speed and acceleration will be
Options
10 cm/s, 10 cm/s2
10 cm/s, 80 cm/s2
40 cm/s, 10 cm/s2
40 cm/s, 40 cm/s2
Advertisements
Solution
(a) 10 cm/s, 10 cm/s2
It is given that the turntable is rotating with uniform angular velocity. Let the velocity be \[\omega\] .
We have:
\[\text{v = r}\omega\]
\[ \Rightarrow \text{v} \propto \text{r} (\text{P for constant }\omega)\]
\[\frac{v}{v'} = \frac{r}{r'}\]
\[ \Rightarrow \text{v}' = \frac{\text{v}}{2} = 10 \text{ cm/s}\]
Similarly, we have: \[a' = \frac{a}{2} = 10\text{ cm/ s}^2\]
APPEARS IN
RELATED QUESTIONS
A 70 kg man stands in contact against the inner wall of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 rev/min. The coefficient of friction between the wall and his clothing is 0.15. What is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed?
A stone of mass m tied to a string of length l is rotated in a circle with the other end of the string as the centre. The speed of the stone is v. If the string breaks, the stone will move
A train A runs from east to west and another train B of the same mass runs from west to east at the same speed along the equator. A presses the track with a force F1 and B presses the track with a force F2.
If the earth stop rotating, the apparent value of g on its surface will
Let θ denote the angular displacement of a simple pendulum oscillating in a vertical plane. If the mass of the bob is m, the tension is the string is mg cos θ
Assume that the earth goes round the sun in a circular orbit with a constant speed of 30 kms
Suppose the amplitude of a simple pendulum having a bob of mass m is θ0. Find the tension in the string when the bob is at its extreme position.
A person stands on a spring balance at the equator. By what fraction is the balance reading less than his true weight?
A track consists of two circular parts ABC and CDE of equal radius 100 m and joined smoothly as shown in figure. Each part subtends a right angle at its centre. A cycle weighing 100 kg together with the rider travels at a constant speed of 18 km/h on the track. (a) Find the normal contact force by the road on the cycle when it is at B and at D. (b) Find the force of friction exerted by the track on the tyres when the cycle is at B, C and. (c) Find the normal force between the road and the cycle just before and just after the cycle crosses C. (d) What should be the minimum friction coefficient between the road and the tyre, which will ensure that the cyclist can move with constant speed? Take g = 10 m/s2.
A table with smooth horizontal surface is fixed in a cabin that rotates with a uniform angular velocity ω in a circular path of radius R (In the following figure). A smooth groove AB of length L(<<R) is made the surface of the table. The groove makes an angle θ with the radius OA of the circle in which the cabin rotates. A small particle is kept at the point A in the groove and is released to move at the point A in the groove and is released to move along AB. Find the time taken by the particle to reach the point B.
Two identical masses are connected to a horizontal thin (massless) rod as shown in the figure. When their distance from the pivot is D, a torque τ produces an angular acceleration of α1. The masses are now repositioned so that they are 2D from the pivot. The same torque produces an angular acceleration α2 which is given by ______
The escape velocity of a body from any planet, whose mass is six times the mass of earth and radius is twice the radius of earth will be
(v8 = escape velocity of a body from the earth's surface).
The real force 'F' acting on a particle of mass ' m' performing circular motion acts along the radius of circle 'r' and is directed towards the centre of circle. The square root of the magnitude of such force is (T = periodic time).
A rigid body is rotating with angular velocity 'ω' about an axis of rotation. Let 'v' be the linear velocity of particle which is at perpendicular distance 'r' from the axis of rotation. Then the relation 'v = rω' implies that ______.
If a cyclist doubles his speed while negotiating a curve, how does the tendency to overturn vary?
An engine is moving on a c1rcular path of radius 200 m with speed of 15 m/s. What will be the frequency heard by an observer who is at rest at the centre of the circular path, when engine blows the whistle with frequency 250 Hz?
A stone tide to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is `sqrt(x("u"^2 - "gL")`. The value of x is ______.
Which of the following statements is FALSE for a particle moving in a circle with a constant angular speed?
Find the angular acceleration of a particle in circular motion which slows down from 300 r.p.m. to 0 r.p.m. in 20 s.
