Question

36) If the error in measurement of momentum of a
particle is 10% and mass is known exactly, the
permissible error in the determination of kinetic
energy is
(1) 20%
(2) 5%
(3) 21%
(4) 10%
(​

Answer 1

20% should be the answer

Answer 2

Explanation,

We know that,

K.E = ¹/2 × mv² ------(1)

Here,

• ¹/2 and m are constants.
• Error depends on the velocity.

Applying momentum formula,

P = mv -----------(2)

Put eqn. (2) value in eqn (1), We get,

K.E = P²/2m

[ Here, error is 10% ]

=> P' = 10% of P

=> P' = 10/100 × P

=> P' = 0.1 P

Now,

=> K.E' = P'/2m

=> K.E' = 1.21 × K.E

=> K.E' = 1.21K.E

We ask to find "Percentage error of kinetic energy".

Percentage error = (Final - Initial) × 100/Initial

[ Put the values ]

=> Percentage error = (1.21K.E - K.E) × 100/K.E

=> Percentage error = 0.21K.E × 100/K.E

=> Percentage error = 0.21 × 100

=> Percentage error = 21%

Therefore,

The permissible error in the determination of kinetic energy is 21%.