Physics

While measuring the time of fall of a body from a height, a person makes an error or $2\%$ in the value of acceleration due to gravity and an error of $4\%$ in the value of height. The percentage error in the measurement of time of fail is?

ANSWER

$3\%$

SOLUTION

Time period of free fall

$t=\sqrt{\dfrac{2h}{g}}$

Take log on both side and differentiate.

$\dfrac{\Delta t}{t}=\dfrac{1}{2}\left( \dfrac{\Delta h}{h}+\dfrac{\Delta g}{g} \right)=\dfrac{1}{2}\left( 0.04+0.02 \right)=0.03$

Hence, error in time is $3\,\%$

You're just one step away

Create your Digital Resume For FREE on your name's sub domain "yourname.wcard.io". Register Here!

Single Correct Medium Published on 18th 08, 2020
Questions 244531
Subjects 8
Chapters 125
Enrolled Students 197

Realted Questions

Q1 Single Correct Medium
The dimensions of voltage in terms of mass $(M)$, length $(L)$ and time $(T)$ and ampere $(A)$ are
• A. $[ML^2T^{-2}A^{-2}]$
• B. $[ML^2T^{3}A^{-1}]$
• C. $[ML^2T^{-3}A^{1}]$
• D. $[ML^2T^{-3}A^{-1}]$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q2 Subjective Medium
The speed of a car increases uniformly from zero to $10\ ms^{-1}$ in $2\ s$ and then remain constant.
a. Find the distance travelled by the car in the first two seconds.
b. Find the distance travelled by the car in next two seconds.
c. Find the total distance travelled in $4\ s$.

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q3 Single Correct Medium
Which of the following pair have same dimensions?
• A. Force and strain
• B. Force and stress
• C. Angular velocity and frequency
• D. Energy and strain

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q4 Single Correct Medium
If $a=8\pm 0.08$ and $b=6\pm 0.06$ let $x=a+b,\quad y=a-b,\quad z=ab$. the correct order of % error in x, y and z is:
• A. $x=y<{ z }$
• B. $x=y>z$
• C. ${ x }<{ z }<{ y }$
• D. ${ x }>{ z }<{ y }$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q5 Single Correct Medium
Subtract $2.5 \times {10}^{4}$ from $3.9 \times {10}^{5}$ and give the answer to correct number of significant figures.
• A.  $3.6\times 10^6$
• B.  $3.6\times 10^5$
• C.  $36\times 10^5$
• D.  $36\times 10^6$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020