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 statements is correct?
- 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
The Correct Option is C
Solution and Explanation
Top Questions on Conservation of energy
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Notes on Conservation of energy
Concepts Used:
Conservation of Energy
In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time.
It also means that energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another. For instance, chemical energy is converted to kinetic energy when a stick of dynamite explodes.
So, mathematically we can represent the law of energy conservation as the following,
The amount of energy spent in a work = The amount of Energy gained in the related work
Now, the derivation of the energy conservation formula is as followed,
Ein − Eout = Δ Esys
We know that the net amount of energy which is transferred in or out of any system is mainly seen in the forms of heat (Q), mass (m) or work (W). Hence, on re-arranging the above equation, we get,
Ein − Eout = Q − W
Now, on dividing all the terms into both the sides of the equation by the mass of the system, the equation represents the law of conservation of energy on a unit mass basis, such as
Q − W = Δ u
Thus, the conservation of energy formula can be written as follows,
Q – W = dU / dt
Here,
Esys = Energy of the system as a whole
Ein = Incoming energy
Eout = Outgoing energy
E = Energy
Q = Heat
M = Mass
W = Work
T = Time