Advertisements
Advertisements
प्रश्न
Figure following shows a light rod of length l rigidly attached to a small heavy block at one end and a hook at the other end. The system is released from rest with the rod in a horizontal position. There is a fixed smooth ring at a depth h below the initial position of the hook and the hook gets into the ring as it reaches there. What should be the minimum value of h so that the block moves in a complete circle about the ring?
उत्तर
Let v be the minimum velocity required to complete a circle about the ring.
Applying the law of conservation of energy,
Total energy at point A = Total energy at point B
\[\text{ mgl } + \frac{1}{2}\text{ mv}^2 = \text{ mg(2l)} + 0\]
\[ \Rightarrow \text{ v } = \sqrt{2\text{ gl }}\]
Let the rod be released from a height h.
Total energy at A = Total energy at B
\[\text{ mgh } = \frac{1}{2}\text{ m } \nu^2 \]
\[\text{ mgh } = \frac{1}{2}\text{m} \left( 2 \text{ gl} \right)\]
So, h = l
APPEARS IN
संबंधित प्रश्न
A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time t is proportional to ______.
A person trying to lose weight (dieter) lifts a 10 kg mass, one thousand times, to a height of 0.5 m each time. Assume that the potential energy lost each time she lowers the mass is dissipated.
- How much work does she do against the gravitational force?
- Fat supplies 3.8 x 107J of energy per kilogram which is converted to mechanical energy with a 20% efficiency rate. How much fat will the dieter use up?
Two inclined frictionless tracks, one gradual and the other steep meet at A from where two stones are allowed to slide down from rest, one on each track . Will the stones reach the bottom at the same time? Will they reach there with the same speed? Explain. Given θ1 = 30°, θ2 = 60°, and h = 10 m, what are the speeds and times taken by the two stones?
A heavy stone is thrown from a cliff of height h with a speed v. The stoen will hit the ground with maximum speed if it is thrown
A heavy stone is thrown in from a cliff of height h in a given direction. The speed with which it hits the ground
(a) must depend on the speed of projection
(b) must be larger than the speed of projection
(c) must be independent of the speed of projection
(d) may be smaller than the speed of projection.
You lift a suitcase from the floor and keep it on a table. The work done by you on the suitcase does not depend on
(a) the path taken by the suitcase
(b) the time taken by you in doing so
(c) the weight of the suitcase
(d) your weight
A small heavy block is attached to the lower end of a light rod of length l which can be rotated about its clamped upper end. What minimum horizontal velocity should the block be given so that it moves in a complete vertical circle?
One end of a spring of natural length h and spring constant k is fixed at the ground and the other is fitted with a smooth ring of mass m which is allowed to slide on a horizontal rod fixed at a height h (following figure). Initially, the spring makes an angle of 37° with the vertical when the system is released from rest. Find the speed of the ring when the spring becomes vertical.
A body is falling freely under the action of gravity alone in vacuum. Which of the following quantities remain constant during the fall?
A mass of 5 kg is moving along a circular path of radius 1 m. If the mass moves with 300 revolutions per minute, its kinetic energy would be ______.
In a shotput event an athlete throws the shotput of mass 10 kg with an initial speed of 1 ms–1 at 45° from a height 1.5 m above ground. Assuming air resistance to be negligible and acceleration due to gravity to be 10 ms–2, the kinetic energy of the shotput when it just reaches the ground will be ______.
Why is electrical power required at all when the elevator is descending? Why should there be a limit on the number of passengers in this case?
A bob of mass m suspended by a light string of length L is whirled into a vertical circle as shown in figure. What will be the trajectory of the particle if the string is cut at
- Point B?
- Point C?
- Point X?
A baloon filled with helium rises against gravity increasing its potential energy. The speed of the baloon also increases as it rises. How do you reconcile this with the law of conservation of mechanical energy? You can neglect viscous drag of air and assume that density of air is constant.
A force shown in the F-x graph is applied to a 5 kg cart, which then coasts up a ramp as shown. The maximum height, ymax is ______ m, at which the cart can reach.
(g = 10 m/s2)
