Question

a particle has kinetic energy of 62 Mev and a momentum of 335 Mev/c.find its rest mass and speed.​

Answer 1

Answer:

The value of the energy attained in the body due to the motion or movement is called kinetic energy. The mathematic formula used to determine the magnitude of the kinetic energy is

K.E=12mv2.

Answer 2

Given info : a particle has kinetic energy of 62 MeV and a momentum of 335 MeV/c.

To find : The rest mass and speed of particle.

solution : using formula, E² = (mc²)² + (pc)²

⇒(62 MeV)² = (mc²)² + (335MeV/c² × c)²

⇒(62 × 1.6 × 10¯¹³ J)² = (mc²)² + (335 × 1.6 × 10¯¹³J/3 × 10^8)²

⇒(99.2 × 10¯¹³)² - (335 × 1.6/3 × 10¯²¹)² = (mc²)²

⇒9.84 × 10¯²³ = {m × (3 × 10^8)²}²

⇒9.9 × 10¯¹² = m × 9 × 10¹⁶

⇒1.1 × 10^-28 = m

Therefore the rest mass would be 1.1 × 10^-28 kg

kinetic energy = 1/2 mv²

⇒62 × 1.6 × 10¯¹³ = 1/2 × 1.1 × 10^-28 × v²

⇒62 × 3.2/1.1 × 10^5 = v²

⇒90.18 × 10⁵ = v²

⇒v ≈ 3 × 10³ m/s

so the speed of the particle is 3 × 10³ m/s