A particle is released from height S from the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the particle be at height $h$ from the surface of the Earth.By the law of conservation of mechanical energy, the total energy at height $S$ is

Vedclass · Accepted Answer

$\frac{S}{4}, \sqrt{\frac{3 gS}{2}}$

Vedclass · Answer

(A) Let the particle be at height $h$ from the surface of the Earth.By the law of conservation of mechanical energy, the total energy at height $S$ is equal to the total energy at height $h$.Total energy $E = mgS$.At height $h$, the potential energy is $PE = mgh$ and kinetic energy is $KE = mg(S-h)$.Given that $KE = 3 PE$, we have $mg(S-h) = 3 mgh$.Dividing by $mg$, we get $S-h = 3h$, which implies $S = 4h$ or $h = S/4$.Now, to find the speed $V$ at this height, we use $KE = \frac{1}{2} mV^2$.Since $KE = 3 PE = 3 mgh = 3 mg(S/4) = \frac{3 mgS}{4}$.Equating the two expressions for $KE$: $\frac{1}{2} mV^2 = \frac{3 mgS}{4}$.Solving for $V$, we get $V^2 = \frac{3 gS}{2}$, so $V = \sqrt{\frac{3 gS}{2}}$.Thus, the height is $S/4$ and the speed is $\sqrt{\frac{3 gS}{2}}$.

$A$ 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:

Similar Questions

According to Robert May,the global species diversity is about ...................

The equation of the straight line perpendicular to $5x - 2y = 7$ and passing through the point of intersection of the lines $2x + 3y = 1$ and $3x + 4y = 6$ is

The force constant of a wire is $k$ and that of another wire is $2k$. When both the wires are stretched through the same distance,then the work done is:

If the starting material for the manufacture of silicones is $RSiCl_{3}$,write the structure of the product formed.

The $T.V.$ transmission tower in Delhi has a height of $245 \ m$. The distance up to which the broadcast can be received (taking the radius of earth to be $6.4 \times 10^6 \ m$) is........$km$ :

Vedclass Test Series

Exam Paper Generator

Online Exam Module