Physics

An equation is given here $$\left(P+\dfrac {a}{V^{2}}\right)=b\dfrac {9}{V}$$ where $$P=$$pressure, $$V=$$Volume and $$\theta=$$Absolute temperature. if $$a$$ and $$b$$ are constants, the dimension of a will be


ANSWER

$$[ML^{5}T^{-2}]$$


SOLUTION

Given that,

Pressure =$$P$$

Volume = $$V$$

Absolute temperature = $$\theta$$

 $$P+\dfrac{a}{{{V}^{2}}}=\dfrac{b\theta }{V}.....(I)$$

Now,

Dimension of $$P= \left[ M{{L}^{-1}}{{T}^{-2}} \right]$$

Dimension of $$V =\left[ {{L}^{3}} \right]$$

Dimension of $$\theta=K$$

Now, from equation (I)

  $$ P+\dfrac{a}{{{V}^{2}}}\Rightarrow a=P{{V}^{2}} $$

 $$ a=\left[ M{{L}^{-1}}{{T}^{-2}} \right]\left[ {{L}^{6}} \right] $$

 $$ a=\left[ M{{L}^{5}}{{T}^{-2}} \right] $$

Hence, the dimension of $$a$$ is $$\left[ M{{L}^{5}}{{T}^{-2}} \right]$$

 

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 201
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
The dimension of angular momentum is
  • A. $$[M^{0}L^{1}T^{-1}]$$
  • B. $$[M^{1}L^{2}T^{-2}]$$
  • C. $$[M^{1}L^{2}T^{-1}]$$
  • D. $$[M^{2}L^{1}T^{-2}]$$

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer
Q2 Single Correct Medium
Magnetic flux and magnetic induction differ in the dimensions of:
  • A. mass
  • B. length
  • C. time
  • D. all of these

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer
Q3 Single Correct Medium
Turpentine oil is flowing through a tube of length l and radius r. The pressure difference between the two ends of the tube is p. The viscosity of oil is given $$\displaystyle \eta = \frac{p(r^2 - x^2)}{4vl}$$, where v is velocity of oil at a distance x from the axis of the tube. The dimensional formula of viscosity is
  • A. $$[M^0 L^0 T^0]$$
  • B. $$[M^1 L^{-1} T^{-1}]$$
  • C. $$[M L^2 T^{-1}]$$
  • D. $$[M^{-1} L^{-1} T^1]$$

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer
Q4 Subjective Medium
Write the number of significant digits in $$1001$$.

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer
Q5 Subjective Medium
Two clocks are being tested against a standard clock located in a national laboratory. At 12:00:00 noon bv the standard clock, the readings of the two clocks are :
Clock 1Clock 2
Monday12:00:0510:15:06
Tuesday12:01:1510:14:59
Wednesday11:59:0810:15:18
Thursday12:01:5010:15:07
Friday11:59:1510:14:53
Saturday12:01:3010:15:24
Sunday12:01:1910:15:11
If you are doing an experiment that requires precision time interval measurements, which of the two clocks will you prefer ?

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer