Advertisements
Advertisements
Question
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 as shown in figure.
Which of the following statement is correct?
Options
Both the stones reach the bottom at the same time but not with the same speed.
Both the stones reach the bottom with the same speed and stone I reaches the bottom earlier than stone II.
Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I.
Both the stones reach the bottom at different times and with different speeds.
Advertisements
Solution
Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I.
Explanation:
As seen in the diagrams, AB and AC are two smooth planes inclined at the angles θ1 and θ2, respectively.
Because there is no friction here, mechanical energy will be preserved.
Because both tracks have the same height h,
`1/2 mv^2 = mg`
`hv = sqrt(2gh)`
Hence, speed is the same for both stones. For stone I, a1 = acceleration along the inclined plane = g sin θ1
Similarly, for stone II, a2 = g sin θ2
And because track II is shorter in length, stone II arrives earlier than stone I.
APPEARS IN
RELATED QUESTIONS
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 block of mass m is attached to two unstretched springs of spring constants k1 and k2 as shown in the following figure. The block is displaced towards the right through a distance x and is released. Find the speed of the block as it passes through the mean position shown.
In the following figure shows two blocks A and B, each of mass of 320 g connected by a light string passing over a smooth light pulley. The horizontal surface on which the block Acan slide is smooth. Block A is attached to a spring of spring constant 40 N/m whose other end is fixed to a support 40 cm above the horizontal surface. Initially, the spring is vertical and unstretched when the system is released to move. Find the velocity of the block A at the instant it breaks off the surface below it. Take g = 10 m/s2.
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.
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?
A particle is released from height S from the surface of the Earth. At a certain height, its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively ______
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 ______.
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 body falls towards earth in air. Will its total mechanical energy be conserved during the fall? Justify.
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 single conservative force acts on a body of mass 1 kg that moves along the x-axis. The potential energy U(x) is given by U (x) = 20 + (x - 2)2, where x is in meters. At x = 5.0 m the particle has a kinetic energy of 20 J, then the maximum kinetic energy of body is ______ J.
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)
