Question

8.
Kinetic energy of a particle depends on the square
of speed of the particle. If error in measurement of
speed is 40% then error in the measurement of
kinetic energy will be
(1) 80%
(2) 40%
(3) 96%
(4) 120%​

Answer 1

★ Solution:-

Kinetic energy is given by the formula ,

$\bigstar\boxed {\mathtt{ KE = \dfrac{1}{2}m {v}^{2} }}$

here ,

• KE = kinetic energy
• m = mass
• v = velocity

From this we can conclude that kinetic energy is directly proportional to the square of velocity

$\bigstar \: \mathtt{ KE \bf{\propto}\ {v}^{2} }$

Initially let the speed of the particle be v

Let the new speed be v n

The error in the measurement of new speed is 40 %

$\implies\mathtt{ v_n = v + \dfrac{40}{100} v}$

$\implies\mathtt{ v_n = v + 0.4 v}$

$\implies\mathtt{ v_n = 1.4v}$

Let's substitute the value of v n in the formula of kinetic energy

$\implies\mathtt{KE_n= \dfrac{1}{2}m{v_n }^{2} }$

$\implies\mathtt{KE_n= \dfrac{1}{2}m{(1.4v)}^{2} }$

$\implies\mathtt{KE_n= \dfrac{1}{2}m{v }^{2} \times 1.96}$

Substituting 1/2 mv² as KE ,

$\implies\mathtt{KE_n= 1.96 \: KE }$

% error in the measurement of kinetic energy

$\implies\mathtt{ \dfrac{KE_n - KE }{KE} ×100}$

$\implies\mathtt{ \dfrac{1.96KE - KE }{KE} ×100}$

$\implies\mathtt{ \dfrac{0.96 \cancel{KE }}{ \cancel{KE}} ×100}$

$\implies\mathtt{96\%}$

The error in measurement of kinetic energy is 96 %

Answer 2

Explanation:

★ Solution:-

Kinetic energy is given by the formula ,

$\bigstar\boxed {\mathtt{ KE = \dfrac{1}{2}m {v}^{2} }}$

KE

n

=1.96KE

% error in the measurement of kinetic energy

\implies\mathtt{ \dfrac{KE_n - KE }{KE} ×100}⟹

KE

KE

n

−KE

×100

bf\implies\mathtt{ \dfrac{1.96KE - KE }{KE} ×100}⟹

KE

1.96KE−KE

×100

[tex]\implies\mathtt{ \dfrac{0.96 \cancel{KE }}{ \cancel{KE}} ×100}⟹

KE

0.96

KE

×100

\implies\mathtt{96\%}⟹96%