In the figure, the ball P is released from rest, when the spring is at its natural length. For the block Q of mass $ 2{{m}_{0}} $ to leave contact with ground at some stage, the minimum mass of P must be
- $ {{m}_{0}} $
- $ 2{{m}_{0}} $
- $ {{m}_{0}}/2 $
- $ {{m}_{0}}/4 $
The Correct Option is A
Solution and Explanation
Top Questions on Conservation of energy
- Determine Min. Energy released when an electron jumps to ground state in Balmer series from infinity.
- JEE Main - 2024
- Physics
- Conservation of energy
- A ball of mass $200\, g$ rests on a vertical post of height $20\, m$ A bullet of mass $10 \,g$, travelling in horizontal direction, hits the centre of the ball After collision both travels independently The ball hits the ground at a distance $30 \,m$ and the bullet at a distance of $120 \,m$ from the foot of the postThe value of initial velocity of the bullet will be (if $g=10\, m / s ^2$ ) :
- JEE Main - 2023
- Physics
- Conservation of energy
- Experimentally it is found that 12.8 eV energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is\(\frac{ 9}{x} x 10^{-10}\)m. The value of the x is _____.
(1eV = 1.6 x 10-19J, \(\frac{1}{4π∈_0}\) = 9 x 109 NM2 / C2 and electronic charge = 1.6 x 10-19JC)- JEE Main - 2023
- Physics
- Conservation of energy
- The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J. The cross sectional area of the wire is______ mm2 . (Given, y = 2.0 x 1011 Nm-2)
- JEE Main - 2023
- Physics
- Conservation of energy
- A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be
- JEE Main - 2023
- Physics
- Conservation of energy
Questions Asked in JCECE exam
- A $ 50\,\Omega $ galvanometer is shunted by a resistance of $ 5\,\Omega . $ The percentage of the total current, which passes through the galvanometer is
- JCECE - 2015
- Current electricity
- The effective resistance across the points P and Q is
- JCECE - 2015
- Current electricity
- A disc of radius a and mass m is pivoted at the rim and is set in small oscillation. If a simple pendulum have the same period as that of the disc, then the length of the simple pendulum should be
- JCECE - 2015
- Oscillations
- An elliptically shaped ring of dimensions shown in figure just touches, the horizontal surface of a liquid of surface tension S. The force required to pull the ring away from the liquid surface is
- JCECE - 2015
- Surface tension
- A physical quantity X is represented by $ X=[{{M}^{\eta }}{{L}^{-\theta }}{{T}^{-\text{o }\!\!|\!\!\text{ }}}]. $ The maximum percentage errors in the measurement of M, L and T, respectively are $ \alpha %,\beta % $ and $ \gamma %. $ The maximum percentage error in the measurement of X will be
- JCECE - 2015
- Units and measurement
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