Question

The percentage error in the measurement of mass and speed are 2% and 3% respectively. Then the

estimated error in the measurement of K.E will be:

a. 4% b. 6% c. 8% d. 10%​

Answer 1

Given :

The percentage error in the measurement of mass and speed are 2% and 3% respectively.

To Find :

Percentage error in the measurement of kinetic energy of body.

Solution :

❖ Kinetic energy of a body of mass m moving at a speed of v is given by, k = 1/2 mv²

» k denotes kinetic energy

» m denotes mass

» v denotes speed

The percentage error in the measurement of kinetic energy is given by

$\bigstar\:\underline{\boxed{\bf{\purple{\dfrac{\Delta k}{k}\times 100=\bigg(\dfrac{\Delta m}{m}+2\dfrac{\Delta v}{v}\bigg)\times 100}}}}$

$\sf:\implies\:\dfrac{\Delta k}{k}\times100=\bigg(\dfrac{\Delta m}{m}\times 100\bigg)+\bigg(2\dfrac{\Delta v}{v}\times100\bigg)$

• ∆m/m × 100 = 2%
• ∆v/v × 100 = 3%

By substituting the given values;

$\sf:\implies\:\dfrac{\Delta k}{k}\times 100=2\%+2(3\%)$

$\sf:\implies\:\dfrac{\Delta k}{k}\times100=2\%+6\%$

$:\implies\:\underline{\boxed{\bf{\orange{\dfrac{\Delta k}{k}\times 100=8\%}}}}$

∴ (C) is the correct answer!

Answer 2

Given :

The percentage error in the measurement of mass and speed are 2% and 3% respectively.

To Find :

Percentage error in the measurement of kinetic energy of body.

Solution :

❖ Kinetic energy of a body of mass m moving at a speed of v is given by, k = 1/2 mv²

» k denotes kinetic energy

» m denotes mass

» v denotes speed

The percentage error in the measurement of kinetic energy is given by

$\bigstar\:\underline{\boxed{\bf{\purple{\dfrac{\Delta k}{k}\times 100=\bigg(\dfrac{\Delta m}{m}+2\dfrac{\Delta v}{v}\bigg)\times 100}}}}$

$\sf:\implies\:\dfrac{\Delta k}{k}\times100=\bigg(\dfrac{\Delta m}{m}\times 100\bigg)+\bigg(2\dfrac{\Delta v}{v}\times100\bigg)$

∆m/m × 100 = 2%

∆v/v × 100 = 3%

By substituting the given values;

$\sf:\implies\:\dfrac{\Delta k}{k}\times 100=2\%+2(3\%)$

$\sf:\implies\:\dfrac{\Delta k}{k}\times100=2\%+6\%$

$:\implies\:\underline{\boxed{\bf{\orange{\dfrac{\Delta k}{k}\times 100=8\%}}}}$

∴ (C) is the correct answer!