Q: A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

Let the speed of the stream be \$x\$ \$km/hr\$Speed downstream \$=(15+x)km/hr\$Speed upstream \$=(15-x)km/hr\$Distance travelled downstream\$=30km\$Distance travelled upstream\$=30km\$Time upstream\$=\dfrac {\text{Distance upstream}}{\text{Speed upstream}}\$Time upstream\$=\dfrac{30}{15-x}\$Time downstream\$=\dfrac {\text{Distance downstream}}{\text{Speed downstream}}\$Time downstream\$=\dfrac{30}{15-x}\$Total time taken \$4.5hrs\$\$4.5=\dfrac{30}{15-x}+\dfrac{30}{15+x}\$\$4.5=\dfrac{30(15+x)+30(15-x)}{225-x^{2}}\$\$4.5=\dfrac{900}{225-x^{2}}\$\$225-x^{2}=200\$\$x^{2}=25\$\$x=5km/hr\$Hence the correct option is (B).

Q: The unit of Stefan's constant \$\sigma\$ is

Stefan's law is \$E=\sigma (T^4)\$\$\Rightarrow \sigma =\dfrac{E}{T^4}\$where,\$E=\dfrac{Energy}{Area \times Time}=\dfrac{Watt}{m^2}\$\$\sigma =\dfrac{Watt-m^2}{k^4}=Watt-m^{-2}k^{-4}\$

Question 1

What do we call the gravitational force between the earth and an object?

Accepted Answer

The gravitation force between the earth and object is called weight.It is also equal to the product of acceleration due to gravity and mass of the object.$Weight = m \times g$,where, $m=$ mass of the object,$g =$ acceleration due to gravity $= 9.8 m/s^{2}$

Question 2

Why do we need standard unit measurement?

Accepted Answer

We need standard unit for measurement to make our judgement more reliable and accurate. For proper dealing, measurement should be same for everybody. Thus there should be uniformity in measurement. For the sake of uniformity we need a common set of units of measurement, which are called standard units. Nowadays Si units in science and technology almost accepted universally.

Question 3

What do you mean by fundamental & derived quantities? Give the derived unit of Force.

Accepted Answer

Fundamental quantity: quantities which are independent on other physical quantity.&#10;&#10;ex: length, mass, time, current, amount of substance, luminous intensity, thermodynamic temperature,&#10;&#10;Derived quantity: quantities which depend on fundamental quantities.&#10;&#10;ex: Area, volume, density, speed, acceleration, force, velocity etcForce is a derived unit if the mass has been declared a fundamental unit. It is the force which imparts to the unit of mass the unit of acceleration. The derived unit of force is $kg.m/s^2$

Question 4

A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

Accepted Answer

Let the speed of the stream be $x$ $km/hr$Speed downstream $=(15+x)km/hr$Speed upstream $=(15-x)km/hr$Distance travelled downstream$=30km$Distance travelled upstream$=30km$Time upstream$=\dfrac {\text{Distance upstream}}{\text{Speed upstream}}$Time upstream$=\dfrac{30}{15-x}$Time downstream$=\dfrac {\text{Distance downstream}}{\text{Speed downstream}}$Time downstream$=\dfrac{30}{15-x}$Total time taken $4.5hrs$$4.5=\dfrac{30}{15-x}+\dfrac{30}{15+x}$$4.5=\dfrac{30(15+x)+30(15-x)}{225-x^{2}}$$4.5=\dfrac{900}{225-x^{2}}$$225-x^{2}=200$$x^{2}=25$$x=5km/hr$Hence the correct option is (B).

Question 5

Write the differences between mass and weight of an object.

Accepted Answer

MassWeight1. The mass of an object is the quantity of matter contained in it.1. The weight of an object is the force with which it is attracted towards the centre of the earth.2. SI unit of mass is kilogram (kg).2. SI unit of mass is kilogram (kg).3. The mass of an object is constant.3. The weight of an object is not constant. It changes with the change in acceleration due to gravity.4. The mass of an object can never be zero.4. The weight of an object can be zero.

Question 6

The unit of Stefan's constant $\sigma$ is

Accepted Answer

Stefan's law is $E=\sigma (T^4)$$\Rightarrow \sigma =\dfrac{E}{T^4}$where,$E=\dfrac{Energy}{Area \times Time}=\dfrac{Watt}{m^2}$$\sigma =\dfrac{Watt-m^2}{k^4}=Watt-m^{-2}k^{-4}$

Question 7

If the unit of force is $100 N,$ unit of length is $10 m$ and unit of time is $100 s$, what is the unit of mass in this system of units?

Accepted Answer

First write the dimension of each quantity and then relate them.Force $[F]=[MLT^{-2}]=100N$............(i)length$[L]=[L]=10m$................(ii)Time $[t]=[T]=100s$..............(iii)Substituting values of L and T from Eqs.(ii) and (iii) in Eq.(i) , we get$M\times 10\times (100) ^{-2}=100$$\Rightarrow=\dfrac{M \times 10}{100 \times 100=100}$$\Rightarrow=M=100 \times 1000 kg=10^5kg$

Question 8

Which of the following is not the fundamental quantity,

Accepted Answer

We know that the fundamental quantities are mass, length and time. velocity = $\dfrac{displacement}{time}$hence velocity is derived quantity

Question 9

What are the differences between the mass of an object and its weight?

Accepted Answer

Mass is the measure of the amount of matter in a body. Weight is the measure of the amount of force acting on a mass due to the acceleration due to gravity.

Question 10

Which of the following is a fundamental unit?

Accepted Answer

Fundamental quantities are those quantities which do not depend on other quantities for their measurement. Current is a fundamental quantity and does not depend on anything else. Ampere is the unit of current. It is a fundamental unit. All other units in the options are of dependent quantities.

Derived Quantities and Units

Language

Rate

REVISE WITH CONCEPTS

Some Examples of Derived Units

QUICK SUMMARY WITH STORIES

Derived Units - with Formulas

Density

What do we call the gravitational force between the earth and an object?

Why do we need standard unit measurement?

What do you mean by fundamental & derived quantities? Give the derived unit of Force.

A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

Write the differences between mass and weight of an object.

The unit of Stefan's constant $σ$ is

If the unit of force is $100 N,$ unit of length is $10 m$ and unit of time is $100 s$ , what is the unit of mass in this system of units?

Which of the following is not the fundamental quantity,

What are the differences between the mass of an object and its weight?

Which of the following is a fundamental unit?

Derived Quantities and Units

Language

Rate

REVISE WITH CONCEPTS

Some Examples of Derived Units

QUICK SUMMARY WITH STORIES

Derived Units - with Formulas

Density

What do we call the gravitational force between the earth and an object?

Why do we need standard unit measurement?

What do you mean by fundamental & derived quantities? Give the derived unit of Force.

A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

Write the differences between mass and weight of an object.

The unit of Stefan's constant σ is

If the unit of force is 100N, unit of length is 10m and unit of time is 100s, what is the unit of mass in this system of units?

Which of the following is not the fundamental quantity,

What are the differences between the mass of an object and its weight?

Which of the following is a fundamental unit?

The unit of Stefan's constant $σ$ is

If the unit of force is $100 N,$ unit of length is $10 m$ and unit of time is $100 s$ , what is the unit of mass in this system of units?