A boy rolls a rubber ball on a wooden surface.
Question: A boy rolls a rubber ball on a wooden surface. The ball travels a short distance before coming to rest. To make the same, ball travel longer distance before coming to rest, he may (a) spread a carpet on the wooden surface (b) cover the ball with a piece of cloth (c) sprinkle talcum powder on the wooden surface (d) sprinkle sand on the wooden surface Solution: (c) Talcum powder reduces friction force and the ball will cover longer distance....
Read More →Using a protractor, draw each of the following angles.
Question: Using a protractor, draw each of the following angles. $130^{\circ}$ Solution: - Draw a straight line AB. - Place a dot at B. This dot represents the vertex of the angle. - Place the centre of the protractor at B and the baseline of the protractor along the arm BA. - Find $130^{\circ}$ on the scale and mark a small dot at the edge of the protractor. - Join the vertex $B$ to the small dot with a ruler to form the second arm, $B C$, of the angle. - Mark the angle with a small arc as show...
Read More →Which of the following statements is incorrect?
Question: Which of the following statements is incorrect? (a) Friction acts on a ball rolling along the ground (b) Friction acts on a boat moving on water (c) Friction acts on a bicycle moving on a smooth road (d) Friction does not act on a ball moving through air Solution: (d) Friction will act in case of ball moving through air always....
Read More →If there is an error of 0.1% in the measurement of the radius of a sphere,
Question: If there is an error of 0.1% in the measurement of the radius of a sphere, find approximately the percentage error in the calculation of the volume of the sphere. Solution: Letxbe the radius andybe the volume of the sphere. $y=\frac{4}{3} \pi x^{3}$ Let $\Delta x$ be the error in the radius and $\Delta y$ be the error in the volume. Then, $\frac{\Delta x}{x} \times 100=0.1$ $\Rightarrow \frac{d x}{x}=\frac{1}{1000}$ Now, $y=\frac{4}{3} \pi x^{3}$ $\Rightarrow \frac{d y}{d x}=4 \pi \mat...
Read More →If there is an error of 0.1% in the measurement of the radius of a sphere,
Question: If there is an error of 0.1% in the measurement of the radius of a sphere, find approximately the percentage error in the calculation of the volume of the sphere. Solution: Letxbe the radius andybe the volume of the sphere. $y=\frac{4}{3} \pi x^{3}$ Let $\Delta x$ be the error in the radius and $\Delta y$ be the error in the volume. Then, $\frac{\Delta x}{x} \times 100=0.1$ $\Rightarrow \frac{d x}{x}=\frac{1}{1000}$ Now, $y=\frac{4}{3} \pi x^{3}$ $\Rightarrow \frac{d y}{d x}=4 \pi \mat...
Read More →If we apply oil on door hinges,
Question: If we apply oil on door hinges, the friction will (a) increase (b) decrease (c) disappear altogether (d) will remain unchanged Solution: (b) The friction will decrease because oil acts as a lubricant which reduce friction....
Read More →A toy car released with the same
Question: A toy car released with the same initial speed will travel farthest on (a) muddy surface (b) polished marble surface (c) cemented surface (d) brick surface Solution: (b) It will go farthest on the surface having least frictional force, i.e. the polished marble surface....
Read More →Using a protractor, draw each of the following angles.
Question: Using a protractor, draw each of the following angles. 60 Solution: - Draw a straight line AB. - Place a dot at B. This dot represents the vertex of the angle. - Place the centre of the protractor at B and the baseline of the protractor along the arm BA. - Find $60^{\circ}$ on the scale and mark a small dot at the edge of the protractor. - Join the vertex B to the small dot with a ruler to form the second arm, BC, of the angle. - Mark the angle with a small arc as shown below....
Read More →To sharpen the blade of a knife by rubbing
Question: To sharpen the blade of a knife by rubbing it against a surface, which of the following will be most suitable? (a) Stone (b) Plastic block (c) Wooden block (d) Class block Solution: (a) Stone will be more suitable because it will exert greater reaction and hence greater friction force which sharpen the blade of a knife easily by rubbing....
Read More →Whenever the surfaces in contact tend
Question: Whenever the surfaces in contact tend to move or move with respect to each other, the force of friction comes into play (a) only if the objects are solid (b) only if one of the two objects is liquid (c) only if one of the two objects is gaseous (d) irrespective of whether the objects are solids, liquids or gases Solution: (d) Force of friction acts in solids, liquids and gases and opposes the motion with respect to each other....
Read More →Find the percentage error in calculating the surface area
Question: Find the percentage error in calculating the surface area of a cubical box if an error of 1% is made in measuring the lengths of edges of the cube. Solution: Letxbe the edge of the cube andybe the surface area. $y=x^{2}$ Let $\Delta x$ be the error in $x$ and $\Delta y$ be the corresponding error in $y$. We have $\frac{\Delta x}{x} \times 100=1$ $\Rightarrow 2 x=\frac{x}{100}$ [Let $d x=\Delta x]$ Now, $y=x^{2}$ $\Rightarrow \frac{d y}{d x}=2 x$ $\therefore \Delta y=\frac{d y}{d x} \ti...
Read More →Find the percentage error in calculating the surface area
Question: Find the percentage error in calculating the surface area of a cubical box if an error of 1% is made in measuring the lengths of edges of the cube. Solution: Letxbe the edge of the cube andybe the surface area. $y=x^{2}$ Let $\Delta x$ be the error in $x$ and $\Delta y$ be the corresponding error in $y$. We have $\frac{\Delta x}{x} \times 100=1$ $\Rightarrow 2 x=\frac{x}{100}$ [Let $d x=\Delta x]$ Now, $y=x^{2}$ $\Rightarrow \frac{d y}{d x}=2 x$ $\therefore \Delta y=\frac{d y}{d x} \ti...
Read More →It is much easier to burst an
Question: It is much easier to burst an inflated balloon with a needle than by a finger. Explain. Solution: Because needle tip has very less area of cross-section in comparison to that of our finger and we know that pressure exerted by a force is inversely proportional to the area where it has been applied, so pressure exerted will be more by the needle tip than the finger....
Read More →Two women are of the same weight.
Question: Two women are of the same weight. One wears sandals with pointed heels while the other wears sandals with flat soles. Which one would feel more comfortable while walking on a sandy beach? Give reasons for your answer. Solution: While walking on a sandy surface, one needs the footwears of larger area so that the pressure exerted on the ground is minimum. So, in this case, the woman having the sandals with pointed heels will be less comfortable in walking while the other woman wears sand...
Read More →An archer shoots an arrow in
Question: An archer shoots an arrow in the air horizontally. However, after moving some distance, the arrow falls to the ground. Name the initial force that sets the arrow in motion. Explain why the arrow ultimately falls down? Solution: The archer shoots an arrow by applying muscular force to stretches the string of the bow. When the string is released, it regains its original position that provides the initial force to set the arrow in motion horizontally. The force of gravity that acts on the...
Read More →A man is pushing a cart down a slope.
Question: A man is pushing a cart down a slope. Suddenly the cart starts moving faster and he wants to sloyy it down. What should he do? Solution: Man can do following things: (i) He can start pulling the cart instead of pushing it in order to balance the downward force due to gravity. (ii) He can go the other side by moving himself very fast in the direction of motion and try to slow down the speed of cart by giving an opposite force to the moving cart....
Read More →Fruits detached from a tree fall down
Question: Fruits detached from a tree fall down due to the force of gravity. We. know, that a force arises due to the interaction between two objects. Name the objects interacting in this case. Solution: The interacting objects in this case are: earth and fruits. Earth applies force of gravity on fruit towards its centre. So, fruit falls down....
Read More →Two thermocol balls held close to each
Question: Two thermocol balls held close to each other but move away from each other, when they are released. Name the force which might be responsible for this phenomenon. Explain. Solution: This is electrostatic force which is created due to the rubbing and since, same charges are induced on two balls, so they move away from each other....
Read More →A chapatti maker is a machine
Question: A chapatti maker is a machine which converts balls of dough into chapatties. What effect of force comes into play in this process? Solution: The force on unit area is called pressure, works on the chapaties. This is the pressure which works on the dough balls and make them chapatties with the help of machine....
Read More →Does the force of gravitation
Question: Does the force of gravitation exist between two astronauts in space? Solution: Yes, there will be gravitational force between the astronauts because every object in universe, whether small or large, exerts a force on every other object, it is the universal law of gravitation....
Read More →A gas filled balloon moves up.
Question: A gas filled balloon moves up. Is the upward force acting on it larger or smaller than the force of gravity? Solution: The upward force will be greater than the force of gravity....
Read More →Does the force of gravity
Question: Does the force of gravity act on dust particles? Solution: Yes, force of gravity acts on the dust particles....
Read More →While sieving grains,
Question: While sieving grains, small pieces fall down. Which force pulls them down? Solution: It is the force of gravity which is responsible for the grains to fall down....
Read More →Find the sum of n terms of the series whose
Question: Find the sum of $n$ terms of the series whose $r^{\text {th }}$ term is $\left(r+2^{r}\right)$. Solution: We need to find the sum of $n$ terms of series whose $r^{\text {th }}$ term is $r+2^{r}$. $a_{r}=r+2^{r}$ So, $n^{\text {th }}$ term, $a_{n}=n+2^{n}$ So, we can find the sum of the series by using summation of the $n^{\text {th }}$ term of the given series. $S_{n}=\sum_{k=1}^{n} a_{k}=\sum_{k=1}^{n} k+2^{k}$ $S_{n}=\sum_{k=1}^{n} a_{k}=\sum_{k=1}^{n} k+\sum_{k=1}^{n} 2^{k} \rightar...
Read More →A circular metal plate expends under heating so that its radius increases by k%.
Question: A circular metal plate expends under heating so that its radius increases byk%. Find the approximate increase in the area of the plate, if the radius of the plate before heating is 10 cm. Solution: Let at any time,xbe the radius andybe the area of the plate. Then, $y=x^{2}$ Let $\Delta x$ be the change in the radius and $\Delta y$ be the change in the area of the plate. We have $\frac{\Delta x}{x} \times 100=k$ When $x=10$, we get $\Delta x=\frac{10 k}{100}=\frac{k}{10}$ Now, $y=\pi x^...
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