Tag: physics

Questions Related to physics

Which of the following pairs of physical quantities have same dimensions?

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. Force and power

  2. Torque and energy

  3. Torque and power

  4. Force and torque

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Correct Option: B
Explanation:
Torque is the moment of force given by:$ \vec\tau=\vec r\times \vec F$

It’s unit is Newton-meter.

The unit of work/energy is also Newton-meter or Joule.

Thus, both of these physical quantities have the same units/dimensions.

$[Torque]=[M][L]^{2}[T]^{−2}=[Energy]$

Which one of the following is not a derived unit?

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. joule

  2. watt

  3. kilogram

  4. newton

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Correct Option: C
Explanation:

Among the given units kilogram is the fundamental or base unit whereas others are the derived units.

Which of the following statements is incorrect regarding mass. ?

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. It is a basic property of matter.

  2. The SI unit of mass is kg.

  3. The mass of an atom is expressed in u.

  4. It depends upon the temperature, pressure or location of the object in space.

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Correct Option: D
Explanation:

Mass is property of mater, which is independent of other properties like temperature, pressure or location of the object in space.

Which of the following is unitless quantity?

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. Pressure gradient

  2. Displacement gradient

  3. Force gradient

  4. Velocity gradient

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Correct Option: B
Explanation:

The gradient of any physical quantity is computed to as per unit length. This means it is a rate with respect to length. So, the Displacement gradient will also be length per unit length. Because a displacement gradient is the ratio of two quantities having dimensions of "length". That is, a displacement gradient has units of a meter per meter for example. 

The length dimensions will be cancelled, and we have a unitless quantity. While others will be having certain units. Hence it is a unitless quantity.

Thus option B is correct.

An atmosphere:

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. Is a unit of pressure

  2. Is a unit of force

  3. Gives an idea of the composition of air

  4. Is the height above which there is no atmosphere

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Correct Option: A
Explanation:

An atmosphere is defined as the unit of pressure because we use to write the atmospheric pressure in terms of the $atm$.


So, it is a unit of pressure. Option $A$ is correct.

In a screw gauge, 5 complete motations of the screw cause it to a linear distance of 0.25 cm. There are 100 circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale divisiors and 30 circular scale divisions. Assuming negligible zero, the thickness of the wire is:

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. $0.4300$ cm

  2. $0.2150$ cm

  3. $0.3150$ cm

  4. $0.0430$ cm

Show answer
Correct Option: B
Explanation:
In one rotation, scale moves $\dfrac{0.25}{5}=0.05\,cm$

Least count $=0.05\times 10^{-2}\,cm$

For $4$main scale division $=4\times 0.05=0.2\,cm$

For circular scale division $30\times 0.05\times 10^{-2}=1.5\times 10^{-2}\,cm$

Thickness of wire $0.2+0.015=0.2150\,cm$

Assuming the length of the day uniformly increases by $0.001$ second per century. The net effect on the measure of time over $20$ centuries is?

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. $3.2$ hour

  2. $2.1$ hour

  3. $2.4$ hour

  4. $5$ hour

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Correct Option: B

$\log _ee^5$ is equal to- 

logarithm and its uses basic mathematical concepts physics

  1. $2.5$

  2. $1.5$

  3. $2$

  4. $5$

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Correct Option: D
Explanation:

$\log _ee^5=5\log _ee=5*1=5$

If $\log _3 x = 3\, & \,\log _x y = 4\,$, then find $y$.

logarithm and its uses basic mathematical concepts physics

  1. ${3^6}$

  2. ${3^9}$

  3. ${3}^{12}$

  4. $none$

Show answer
Correct Option: C
Explanation:

We have,

${{\log } _{3}}x=3$

 

We know that

${{\log } _{a}}x=y\Rightarrow x={{a}^{y}}$

 

Therefore,

$ x={{3}^{3}} $

$ x=27 $

 

Here,

$ {{\log } _{x}}y=12 $

$ y={{x}^{12}} $

 

On putting the value of $x$, we get

$y={{3}^{12}}$

 

Hence, this is the answer.

If anti ${ \log } _{ 10 }(0.3678)=2.3324$ then ${ \log } _{ 10 }233.2$ is equal to

logarithm and its uses basic mathematical concepts physics

  1. 367.8

  2. 36.78

  3. 3.3678

  4. 2.3678

Show answer
Correct Option: D
Explanation:

$antilog _{10}(0.3678)=2.3324$


$\therefore \log(2.3324)=0.3678$

$\log _{10}233.2=\log _{10}(2.332\times 100)$

                     $=\log _{10}(2.332) + \log (10^2) \quad \dots ( \log a+\log b=\log(ab))$

                     $=\log _{10}(2.332) + 2\log (10) \quad \dots ( n \log _ab=\log _ab^n)$

As we know, $log _a a=1$

$\log _{10}233.2=2+0.3678=2.3678$