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Physics Case study (4 Marks)

Introduction to Physics · UP Board (UPMSP) STD 11 Science (UPMSP - English Medium). 6 questions.

Questions

Case study (4 Marks)

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6 questions · 1 auto-graded MCQ + 5 self-marked written.

Question 14 Marks
A dimensionless quantity:
  1. Never has a unit.
  2. Always has a unit
  3. May have a unit.
  4. Does not exist.
Answer
  1. May have a unit.
Explanation:

Dimensionless quantities may have units.
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Question 24 Marks
Which of the following sets cannot enter into the list of fundamental quantities in any system of units?
  1. Length, mass and velocity.
  2. Length, time and velocity.
  3. Mass, time and velocity.
  4. Length, time and mass.
Answer
  1. Length, time and velocity.
Explanation:

We define length and time separately as it is not possible to define velocity without using these quantities. This means that one fundamental quantity depends on the other. So, these quantities cannot be listed as fundamental quantities in any system of units.
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Question 34 Marks
The dimensions $\text{ML}^{-1}\text{T}^{-2}$ may correspond to:
  1. Work done by a force.
  2. Linear momentum.
  3. Pressure.
  4. Energy per unit volume.
Answer
  1. Pressure.
  2. Energy per unit volume.
Explantion:

$\text{[Work done] = [ML}^2\text{ T}^{-2}]$

$\text{[Linear momentum] = [MLT}^{-1}]$

$\text{[Pressure] = [ML}^{-1}\text{T}^{-2}]$

$\text{[Energy per unit volume] = [ML}^{-1}\text{T}^{-2}]$

From the above, we can see that pressure and energy per unit volume have the same dimension, i.e., $\text{ML}^{-1}\text{T}^{-2}.$
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Question 44 Marks
A unitless quantity:
  1. Never has a non-zero dimension.
  2. Always has a non-zero dimension.
  3. May have a non-zero dimension.
  4. Does not exist.
Answer
  1. Never has a non-zero dimension.
Explanation:

A unitless quantity never has a non-zero dimension.
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Question 54 Marks
A physical quantity is measured and the result is expressed as nu where u is the unit used and n is the numerical value. If the result is expressed in various units then:
  1. $\text{n}\propto\text{size of u}$
  2. $\text{n}\propto\text{u}^2$
  3. $\text{n}\propto\sqrt{\text{u}}$
  4. $\text{n}\propto\frac{1}{\text{u}}$
Answer
  1. $\text{n}\propto\frac{1}{\text{u}}$
Explanation:

The larger the unit used to express the physical quantity, the lesser will be the numerical value.

Example: 1kg of sugar can be expressed as 1000g or 10000mg of sugar.

Here, g (gram) is the larger quantity as compared to mg (milligram), but the numerical value used with gram is lesser than the numerical value used with milligram.
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MCQ 64 Marks
$\int\frac{\text{dx}}{\sqrt{2\text{ax}-\text{x}^2}}=\text{a}^{\text{n}}\sin^{-1}\Big[\frac{\text{x}}{\text{a}}-1\Big].$ The value of n is:
  • ✓
    $0$
  • B
    $-1$
  • C
    $1$
  • D
    None of these.
Answer
Correct option: A.
$0$
$[ax] = [x^2]$
$\Rightarrow [a] = [x] ...(1)$
Dimension of $\text{LHS} =$ Dimension of $\text{RHS}$
$\Rightarrow\Big[\frac{\text{dx}}{\sqrt{\text{x}}^2}\Big]=\big[\text{a}^{\text{n}}\big]$
$\Rightarrow\Big[\frac{\text{L}}{\text{L}}\Big]=\big[\text{a}^{\text{n}}\big] \ ...(2)$
$\Rightarrow\big[\text{L}^{0}\big]=[\text{a}^{\text{n}}]$
$\text{n}=0$
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