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

$A$ man weighing $60\, kg$ stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude $0.1\, m$ and frequency $\frac{2}{\pi }\, Hz$. Which of the following statements is correct?

How many atoms of calcium will be deposited from a solution of $CaCl_2$ by a current of $25 \ mA$ flowing for $60 \ s$?

Which of the following is an amorphous solid?

The truth table for the system of four $NAND$ gates as shown in the figure is:

The outer and inner radii of a hollow cylinder are $(4.23 \pm 0.01) \text{ cm}$ and $(3.89 \pm 0.01) \text{ cm}$ respectively. What is the thickness of the wall of the cylinder?

Vedclass Test Series

Exam Paper Generator

Online Exam Module