Physics

# The SI unit of energy is $J=kg\ { m }^{ 2 }\ { s }^{ -2 }$; that of speed $v$ is $m{ s }^{ -1 }$ and of acceleration $a$ is $m{ s }^{ -2 }$. Which of the formula for kinetic energy ($K$) given below can you rule out on the basis of dimensional arguments ($m$ stands for the mass of the body):

$K={ (1 / 2) } m{ v }^{ 2 }$

$K= { (3 / 16) } m{ v }^{ 2 }$

##### SOLUTION
The dimensional formula for K.E is $\left[{M}^{1}{L}^{2}{T}^{-2}\right]$
According to the principle of homogeneity of dimensional analysis, the dimensions of each term on both the sides of correct formula or equation will be the same.
The dimensions of quantity on R.H.S of different quantities are
$(a)\left[{M}^{2}{L}^{3}{T}^{-3}\right]$
$(b)\left[{M}^{1}{L}^{2}{T}^{-2}\right]$
$(c)\left[{M}^{1}{L}^{1}{T}^{-2}\right]$
$(d)\left[{M}^{1}{L}^{2}{T}^{-2}\right]$
$(e)\left[{M}^{1}{L}^{2}{T}^{-2}\right]+\left[{M}^{1}{L}^{1}{T}^{-2}\right]$
Since dimensional formula of the R.H.S of $(a),(c)$ and both the terms of R.H.S of $(e)$ are not the same as that of L.H.S i.e.,$\left[{M}^{1}{L}^{2}{T}^{2}\right]$
$\therefore$ the formulae $(a),(c)$ and $(e)$ are ruled out dimensionally.

You're just one step away

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

Multiple Correct Medium Published on 18th 08, 2020
Questions 244531
Subjects 8
Chapters 125
Enrolled Students 203

#### Realted Questions

Q1 Single Correct Easy
Identify which of the following statements is true?
• A. Displacement is a scalar and distance is a vector.
• B. Displacement is a vector and distance is scalar.
• C. Both displacement and distance are vectors.
• D. Neither displacement nor distance the vectors
• E. Displacement and distance are slangs equal

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q2 Subjective Medium
A physical parameter a can be determined by measuring the parameters b, c, d and e using the relation $a = b^{\alpha} c^{\beta} d^{\gamma} e^{\delta}$. If the maximum errors in the measurement of b, c, d and e are $b_1\%, c_1\%, d_1\%$ and $e_1\%$, then find the maximum error in the value of a determined by the experiment.

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q3 Single Correct Hard
The most accurate reading of the length of a $6.28cm$ long fibre is
• A. $6cm$
• B. $6.5cm$
• C. $5.99cm$
• D. $6.0cm$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q4 Single Correct Medium
The dimensions of $\displaystyle \frac{a}{b}$ in the equation $\displaystyle P= \frac{a-t^{2}}{bx},$ where $P$ is pressure, $x$ is distance and $t$ is time, are
• A. $\displaystyle \left [ M^{2}LT^{-3} \right ]$
• B. $\displaystyle \left [ MT^{-2} \right ]$
• C. $\displaystyle \left [ LT^{-3} \right ]$
• D. $\displaystyle \left [ ML^{3}T^{-1} \right ]$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q5 Single Correct Medium
If $y = sin\theta$, then for what value of $\theta$, the relative error in y is minimum?
• A. $90^0$
• B. $30^0$
• C. $0^0$
• D. $45^0$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020