## The volume of a 500 g sealed packet

[question] Question. The volume of a $500 \mathrm{~g}$ sealed packet is $350 \mathrm{~cm}^{3}$. Will the packet float or sink in water if the density of water is $1 \mathrm{~g} \mathrm{~cm}^{3}$ ? What will be the mass of the water displaced by this packet ? [/question] [solution] Solution: Given, mass of sealed packet, m = 500 g ; volume, $\mathrm{V}=350 \mathrm{~cm}^{3} ;$ density, $\rho=?$ density of water, $\rho_{w}=1 \mathrm{~g} \mathrm{~cm}^{-3}$ Density $=\frac{\text { Mass }}{\text { Vol...

## The volume of 50 g of a substance

[question] Question. The volume of $50 \mathrm{~g}$ of a substance is $20 \mathrm{~cm}^{3}$. If the density of water is $1 \mathrm{~g} \mathrm{~cm}^{-3}$, will the substance float or sink in water ? [/question] [solution] Solution: Given, mass of substance, $m=50$ g; volume, $\mathrm{V}=20 \mathrm{~cm}^{3} ;$ density, $\rho=?$ Density $=\frac{\text { Mass }}{\text { Volume }}=\frac{50}{20}=2.5 \mathrm{~g} \mathrm{~cm}^{-3}$ The density of the substance is more than the density of water $\left(1 ...

## Why does a block of plastic released under water come up to the surface of water ?

[question] Question. Why does a block of plastic released under water come up to the surface of water ? [/question] [solution] Solution: Density of plastic block is less than the density of water. Thus, when it floats, it is partially immersed in water such that its weight gets balanced with the buoyant force acting on it. When it is put completely in water, buoyant force on it becomes more than its weight. Thus, when it is released, it comes up to the surface of the water due to a net upward fo...

## In what direction does the buoyant force on an object immersed in a liquid act ?

[question] Question. In what direction does the buoyant force on an object immersed in a liquid act ? [/question] [solution] Solution: An object immersed in a liquid experiences a buoyant force in upward direction. [/solution]...

## A ball thrown up vertically returns to the thrower after 6 s. Find.

[question] Question. A ball thrown up vertically returns to the thrower after 6 s. Find. (a) the velocity with which it was thrown up (b) the maximum height it reaches, and (c) its position after 4 s (take g = 10 m/s2) [/question] [solution] Solution: (a) The ball returns to the thrower in 6 s, thus, the time for its upward journey = 6 ÷ 2 = 3 s For the upward motion of ball, initial velocity u = ? ; final velocity v = 0 ( $\because$ Ball comes to rest) Time, t = 3 s Acceleration due to gravity,...

## Calculate the force of gravitation between the earth and the Sun,

[question] Question. Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth $=6 \times 10^{24} \mathrm{~kg}$ and of the Sun $=2 \times 10^{30} \mathrm{~kg}$. The average distance between the two is $1.5 \times 10^{11} \mathrm{~m}$. [/question] [solution] Solution: Given mass of earth, $\mathrm{M}_{\mathrm{e}}=6 \times 10^{24} \mathrm{~kg} ;$ mass of Sun, $\mathrm{M}_{\mathrm{s}}=2 \times 10^{30} \mathrm{~kg} ;$ distance between them, $\mathrm{r}=1.5 \t...

## A stone is thrown vertically upward with an initial velocity of 40 ms–1. Taking g = 10 ms–2,

[question] Question. A stone is thrown vertically upward with an initial velocity of 40 ms–1. Taking g = 10 ms–2, find the maximum height reached by the stone. What is the net displacement and the total distance covered by the stone ? [/question] [solution] Solution: Initial velocity of stone $\mathrm{u}=40 \mathrm{~ms}^{-1}$ final velocity of stone v = 0 ; acceleration due to gravity $g=-10 \mathrm{~ms}^{2}$ [For upward direction g is taken –ve] ; height attained by stone (h) = ? We, know, $\ma...

## A stone is released from the top of a tower of height 19.6 m.

[question] Question. A stone is released from the top of a tower of height 19.6 m. Calculate its final velocity just before touching the ground. [/question] [solution] Solution: Initial velocity of stone, $\mathrm{u}=0 ;$ final velocity of stone, v = ? height, $\mathrm{h}=19.6 \mathrm{~m}$; acceleration due to gravity, $\mathrm{g}=+9.8 \mathrm{~ms}^{-2}$ We know, $v^{2}=u^{2}+2 g h$ $\mathrm{v}^{2}=(0)^{2}+2 \times 9.8 \times 19.6$ or $\mathrm{v}^{2}=19.6 \times 19.6$ $v=\sqrt{19.6 \times 19.6}=...

## A ball is thrown vertically upwards with a velocity of 49 ms–1.

[question] Question. A ball is thrown vertically upwards with a velocity of 49 ms–1. Calculate (i) The maximum height to which it rises. (ii) The total time it takes to return to the surface of the earth. [/question] [solution] Solution: (i) Initial velocity of the ball, $\mathrm{u}=49 \mathrm{~ms}^{-1}$ Final velocity of the ball, $\mathrm{v}=0$ Acceleration due to gravity $g=-9.8 \mathrm{~ms}^{-2}$ [In upward direction, $g$ is taken -ve] Height attained by the ball, $\mathrm{s}=$ ? Time for ri...

## Gravitational force on the surface of the Moon is only

[question] Question. Gravitational force on the surface of the Moon is only $\frac{1}{6}$ as strong as gravitational force on the earth. What is the weight in newton of a $10 \mathrm{~kg}$ object on the Moon and on the earth ? [/question] [solution] Solution: Mass of object $(\mathrm{m})=10 \mathrm{~kg}$ Acceleration due to gravity on earth (g) $=9.81 \mathrm{~ms}^{-2}$. Acceleration due to gravity on Moon $\left(g_{\mathrm{m}}\right)=\frac{9.81}{6} \mathrm{~ms}^{-2}$ Weight of the object on the...

## Why will a sheet of paper fall slower than one that is crumpled into a ball ?

[question] Question. Why will a sheet of paper fall slower than one that is crumpled into a ball ? [/question] [solution] Solution: Sheet crumpled into a ball has small surface area as compared to the similar unfolded sheet. Therefore, unfolded sheet will experience more resistance due to air as compared to the sheet crumpled into a ball, inspite of same force of gravity acting upon them. It is larger resistance of air which slows down the unfolded sheet, and therefore it falls slower as compare...

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

[question] Question. What do we call the gravitational force between the earth and an object ? [/question] [solution] Solution: It is called force of gravity [/solution]...

## What is the acceleration of free fall ?

[question] Question. What is the acceleration of free fall ? [/question] [solution] Solution: The acceleration of free fall for object moving near the surface of earth is $9.81 \mathrm{~ms}^{-2}$. [/solution]...

## What is the importance of universal law of gravitation ?

[question] Question. What is the importance of universal law of gravitation ? [/question] [solution] Solution: Importance of universal law of gravitation is as follows : (i) It is the gravitational force between the Sun and the earth, which makes the earth move around the Sun. (ii) The tides formed in sea are because of gravitational pull exerted by the Sun and the Moon on the surface of water. (iii) It is the gravitational pull of earth, which keeps us and other bodies firmly on the ground. (iv...

## What happens to the force between two objects, if

[question] Question. What happens to the force between two objects, if (i) the mass of one object is doubled ? (ii) the distance between the objects is doubled and tripled ? (iii) the masses of both objects are doubled ? [/question] [solution] Solution: (i) The force of gravitation doubles. (ii) The force of gravitation decreases 4 times if the distance between the objects is doubled, and if the distance between the objects is tripled then the force of gravitation decreases 9 times. (iii) The fo...

## If the Moon attracts the earth, why does the earth not move towards the Moon ?

[question] Question. If the Moon attracts the earth, why does the earth not move towards the Moon ? [question] [solution] Solution: The earth does not move towards the Moon because the force exerted by the earth or the Moon on each other is insufficient to move the earth, on account of its huge mass....

## The earth and the Moon are attracted to each other by gravitational force.

[question] Question. The earth and the Moon are attracted to each other by gravitational force. Is the force with which the earth attracts the Moon greater, smaller or the same as the force with which the Moon attracts the earth ? Why ? [question] [solution] Solution: The earth attracts the Moon with the same force with which the Moon attracts the earth because, the gravitational forces between any two bodies are equal and opposite (Newton's third law). [solution]...

## What is the magnitude of the gravitational force between the earth

[question] Question. What is the magnitude of the gravitational force between the earth and a $1 \mathrm{~kg}$ object on its surface? (Mass of the earth is $6 \times 10^{24} \mathrm{~kg}$ and radius of the earth is $6.4 \times 10^{6} \mathrm{~m}$.) [/question] [solution] Solution: $\mathrm{F}_{\mathrm{g}}=\frac{\mathrm{G} \times \mathrm{M} \times \mathrm{m}}{\mathrm{R}^{2}}$ Where, M = mass of the earth ; m = mass of object; R = radius of earth. $\mathrm{F}_{8}=\frac{6.67 \times 10^{-11} \times\...

## Gravitational force acts on all objects in proportion to their masses.

[question] Question. Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object ? [/question] [solution] Solution: A freely falling object of any mass falls under the action of gravity given by $g=\frac{G M}{r^{2}}$, where $^{\prime} G^{\prime}$ is constant of gravitation, M is mass of earth, r is the distance between the object and the centre of earth. Thus, the acceleration due to gravity is independent of the mass o...

## How does the force of gravitation between two objects

[question] Question. How does the force of gravitation between two objects change when the distance between them is reduced to half ? [/question] [solution] Solution: When all other variables remain constant, the force of gravitation is inversely proportional to the square of distance between the two objects. $F \propto \frac{1}{r^{2}} \Rightarrow \frac{F^{\prime}}{F}=\frac{r^{2}}{\left(\frac{r}{2}\right)^{2}}=\frac{4 r^{2}}{r^{2}}=4$ $\therefore$ The force of gravitation increases 4 times. [sol...

## You have a bag of cotton and an iron bar,

[question] Question. You have a bag of cotton and an iron bar, each indicating a mass of 100 kg when measured on a weighing machine. In reality, one is heavier than other. Can you say which one is heavier and why ? [solution] Solution: A weighing machine measures the apparent weight of an object. We know that apparent weight $\left(\mathrm{W}_{2}\right)$ is equal to true weight $\left(\mathrm{W}_{2}\right)$ minus buoyant force $\left(\mathrm{F}_{\mathrm{B}}\right)$ i.e., $\mathrm{W}_{\mathrm{a}}...

## You find your mass to be 42 kg

[question] Question. You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg ? [/question] [solution] Solution: When you weigh your body, an upward buoyant force acts on your body due to the air (a fluid) present around you. As a result, the body gets pushed slightly upwards, causing the weighing machine to show a reading slightly less than the actual value. [/solution]...

## Why does an object float or sink when placed on the surface of water ?

[question] Question. Why does an object float or sink when placed on the surface of water ? [/question] [solution] Solution: If the density of an object is more than the density of the liquid, then it sinks in the liquid. This is because the buoyant force acting on the object is less than the weight of the object. If the density of the object is less than or equal to the density of the liquid, then it floats on the surface of the liquid. This is because the buoyant force acting on the object is ...

## Why is it difficult to hold a school bag having a strap made of a thin and strong string ?

[question] Question. Why is it difficult to hold a school bag having a strap made of a thin and strong string ? [question] [solution] Solution: It is difficult to hold a school bag having a thin strap because the pressure on the shoulders is quite large. This is because the pressure is inversely proportional to the area on which the force acts. The smaller is the area, the larger will be the pressure on the surface. In the case of a thin strap, the contact area is very small. Hence, the pressure...

## Why is the weight of an object

[question] Question. Why is the weight of an object on the Moon $\frac{1}{6}$ th of its weight on the earth ? [/question] [solution] Solution: Acceleration due to gravity $\left(\mathrm{g}_{\mathrm{m}}\right)$ on Moon is $\frac{1}{6}$ th of the acceleration due to gravity $\left(\mathrm{g}_{\mathrm{e}}\right)$ on earth. i.e., $\mathrm{g}_{\mathrm{m}}=\frac{1}{6} \mathrm{~g}_{\mathrm{e}}$ or $m g_{\mathrm{m}}=\frac{1}{6} \mathrm{mg}_{\mathrm{e}} \quad$ where, $\mathrm{m}=$ mass of object or $\qua...

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

[question] Question. What are the differences between the mass of an object and its weight ? [/question] [solution] Solution: [/solution]...

## What do you mean by acceleration due to gravity?

[question] Question. What do you mean by acceleration due to gravity? [/question] [solution] Solution: The acceleration produced in a body due to force of gravity is called acceleration due to gravity. It is denoted by g. The value of acceleration due to gravity is taken as 9.8 ms–2 at the sea level. [/solution]...

## What do you mean by free fall ?

[question] Question. What do you mean by free fall ? [/question] [solution] Solution: When an object moves with a constant acceleration, under the influence of force of gravitation of the earth only, the object is said to have free fall. [/solution]...

## Write the formula to find the magnitude of the gravitational force between t.

[question] Question. Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth. [question] [solution] Solution: $\mathrm{F}_{\mathrm{g}}=\frac{\mathrm{GMm}}{\mathrm{R}^{2}}$ Where G is gravitational constant, M is the mass of the earth, m is the mass of the object, R is the distance between the centre of the object and the centre of the earth radius of earth. [solution]...

## State the universal law of gravitation.

[question] Question. State the universal law of gravitation. [/question] [solution] Solution: Every body in this universe attracts every other body with a force, which is directly proportional to the product of their masses and inversely proportional to the square of distance between their centres [/solution]...