Physics

If force $$F$$, length $$L$$ and time $$T$$ are chosen as fundamental quantities, then the dimensional formula for mass is:


ANSWER

$${ F }^{ 1 }{ L }^{ -1 }{ T }^{ 2 }$$


SOLUTION
Mass $$=M^{1}L^{0}T^{0}=F^{\alpha}L^{\beta}T^{\gamma}$$
$$M^{1}L^{0}T^{0}=(MLT^{2})^{\alpha}(L)^{\beta}(T)^{\gamma}$$
$$M^{1}L^{0}T^{0}=M^{\alpha}L^{\alpha+\beta}T^{-2\alpha+\gamma}$$
$$\alpha=1,\alpha+\beta=0 \Rightarrow \beta=-1$$
$$-2 \alpha + \gamma=0$$
$$\Rightarrow \gamma =2$$
$$\Rightarrow Mass = F^{1}L^{-1}T^{2}$$
View Answers

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
Next Question
Questions 244531
Subjects 8
Chapters 125
Enrolled Students 218
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
Find the dimensions of
1) Force
2) power
3) density
4) momentum
5) velocity

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer
Q2 Single Correct Medium
The density of a cube is measured by measuring its mass ad length of its side. If the maximum errors in the measurement of its mass and length are $$3\%$$ and $$2\%$$ respectively, the maximum error in the measurement of density would be:
  • A. $$12\%$$
  • B. $$14\%$$
  • C. $$7\%$$
  • D. $$9\%$$

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer
Q3 Single Correct Medium
A vessel has $$x$$ $$g$$ of gas at high pressure $$P$$. When certain gas escapes, the pressure $$P$$ became $$P/8$$ and temperature $$T$$ became $$2T$$. What is the amount of gas escaped?
  • A. $$\frac23m$$
  • B. $$\frac13m$$
  • C. $$\frac{15}{16}m$$
  • D. $$\frac34m$$

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer
Q4 Single Correct Hard
A student measures the time period of $$100$$ oscillations of a simple pendulum four times. The data set is $$90\ s, 91\ s, 95\ s$$ and $$92\ s$$. If the minimum division in the measuring clock is $$1\ s$$, then the reported mean time should be:
  • A. $$92\pm 2\ s$$
  • B. $$92\pm 5.0\ s$$
  • C. $$92\pm 1.8\ s$$
  • D. $$92\pm 3\ s$$

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer
Q5 Single Correct Medium
The velocity $$v$$ of a particle at time$$ t$$ is given by $$\displaystyle v = at + \frac {b} {t + c} $$ where $$a, b$$ and $$c$$ are constants. The dimensions of $$a, b$$ and $$c$$ are respectively :
  • A. $$ LT^{-2}\, , L $$ and $$\displaystyle T $$
  • B. $$ L^{2}\, , T $$ and $$\displaystyle LT^{2} $$
  • C. $$ LT^{2}\, , LT $$ and $$\displaystyle L $$
  • D. $$ L\, , LT $$ and $$\displaystyle T^{2} $$

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer