Questions Related to NCERT

The gravitational force between the Earth and an object is called the weight of the object.

This is a specific type of gravitational force, which is the universal attractive force that exists between any two objects with mass.

The acceleration produced in a body when it falls freely under the influence of gravity alone is called the acceleration due to gravity or acceleration of free fall.
It is denoted by g and its value on Earth is approximately 9.8 m/s².
This means that the velocity of a freely falling object increases by 9.8 m/s every second.

The universal law of gravitation explains many natural phenomena. Its importance is as follows:

1. It helps us understand how all objects in the universe attract each other.
2. It explains the motion of the Moon around the Earth and the motion of planets around the Sun.
3. It helps us understand the cause of tides due to the gravitational pull of the Moon and the Sun.
4. It explains why objects fall towards the Earth when dropped.

Thus, the universal law of gravitation helps us understand and explain the structure and behavior of the universe.

Both the Earth and the Moon attract each other with equal gravitational force, but the Earth does not move noticeably towards the Moon because the mass of the Earth is much greater than the mass of the Moon.
Due to its very large mass, the acceleration produced in the Earth is extremely small, while the lighter Moon moves more easily around the Earth.

The Earth attracts the Moon with a force equal in magnitude to the force with which the Moon attracts the Earth.
According to Newton’s Third Law of Motion, every action has an equal and opposite reaction.
Therefore, the gravitational force of the Earth on the Moon and the gravitational force of the Moon on the Earth are equal in size but opposite in direction.

The formula for gravitational force is:
F = G × (m₁ × m₂) / r²

Here,
G = 6.67 × 10⁻¹¹ N·m²/kg²
m₁ = 6 × 10²⁴ kg
m₂ = 1 kg
r = 6.4 × 10⁶ m

F = (6.67 × 10⁻¹¹ × 6 × 10²⁴ × 1) / (6.4 × 10⁶)²
F = (4.002 × 10¹⁴) / (4.096 × 10¹³)
F = 9.77 N

Therefore, the gravitational force between the Earth and the object is approximately 9.8 N.

Although the gravitational force on a heavy object is greater because of its larger mass, the acceleration due to gravity is the same for all objects.
The acceleration due to gravity (g = 9.8 m/s²) does not depend on the mass of the object.
Therefore, both heavy and light objects fall at the same rate when only gravity acts on them (if air resistance is ignored).

According to the law of gravitation, the force of attraction between two objects is inversely proportional to the square of the distance between them.
When the distance is reduced to half, the new force becomes four times greater than before.
So, the gravitational force increases byfour times.

Area of square = m × m = m²
Area of triangle = ½ × base × height = ½ × m × m = ½m²

Total area = m² + ½m² = 3/2 m²

Final Answer: 3/2 m²

The husk of coconut is made up of sclerenchyma tissue.
This tissue is made of dead cells with thick walls and provides strength and protection.

Mass = 10 kg
Height = 80 cm = 0.8 m
Acceleration due to gravity (g) = 10 m/s²
Initial velocity = 0 (since it falls from rest)

Step 1: Find final velocity before hitting the floor
Use the formula:
v² = u² + 2gh
v² = 0 + 2 × 10 × 0.8 = 16
v = √16 = 4 m/s

Step 2: Find momentum
Momentum = mass × velocity
= 10 × 4 = 40 kg·m/s

Hence the dumb-bell transfers 40 kg·m/s of momentum to the floor.

Rahul is correct.

According to Newton's Third Law of Motion, every action has an equal and opposite reaction. This means that the force the motorcar exerts on the insect is equal in magnitude and opposite in direction to the force the insect exerts on the motorcar.
Both the insect and the car experience the same force and the same change in momentum (but in opposite directions).
However, since the insect has a much smaller mass, it undergoes a large change in velocity and gets damaged. The car, being much heavier, shows no noticeable change in motion.

Kiran is wrong because change in momentum depends on both mass and velocity. Even though the insect’s velocity changes more, its small mass results in a smaller change in  momentum.

Akhtar is also wrong because the force is not greater on the insect alone. Both the insect and the car experience the same force.

Mass (m) = 100 kg
Initial velocity (u) = 5 m/s
Final velocity (v) = 8 m/s
Time (t) = 6 s

1.Initial momentum = mass × initial velocity
                                         = 100 × 5 = 500 kg·m/s

2. Final momentum = mass × final velocity
                                       = 100 × 8 = 800 kg·m/s

3. Force = rate of change of momentum
     Force = (Final momentum – Initial momentum) ÷ time
                 = (800 – 500) ÷ 6
                 = 300 ÷ 6 = 50 N

Mass of moving object = 1 kg
Velocity of moving object = 10 m/s
Mass of wooden block = 5 kg
Velocity of wooden block = 0 m/s

Total momentum before impact = (1 × 10) + (5 × 0) = 10 kg·m/s

Let the combined velocity after impact be v
Total mass after impact = 1 + 5 = 6 kg
Using conservation of momentum:
Total momentum after impact = 6 × v
So, 10 = 6 × v
v = 10 ÷ 6 = 1.67 m/s (approximately)

Total momentum after impact = 6 × 1.67 = 10 kg·m/s

Hence -
Total momentum before impact = 10 kg·m/s
Total momentum after impact = 10 kg·m/s
Velocity of the combined object = 1.67 m/s

Mass = 10 g = 0.01 kg
Initial velocity (u) = 150 m/s
Final velocity (v) = 0 m/s
Time (t) = 0.03 s

Step 1: Find acceleration (a)
Use the formula:
v = u + at
0 = 150 + a × 0.03
a = -150 ÷ 0.03 = -5000 m/s²

Step 2: Find distance (s)
Use the formula:
s = ut + (1/2)at²
s = 150 × 0.03 + (1/2) × (-5000) × (0.03)²
s = 4.5 - 2.25 = 2.25 m

Step 3: Find force (F)
Use the formula:
F = m × a
F = 0.01 × (-5000) = -50 N
(Magnitude of force = 50 N)

Hence the distance of penetration = 2.25 m and magnitude of force = 50 N

Mass of the ball = 200 g = 0.2 kg
Initial velocity = 10 m/s
Final velocity = -5 m/s (negative because it moves in the opposite direction)

Initial momentum = 0.2 × 10 = 2 kg·m/s
Final momentum = 0.2 × (-5) = -1 kg·m/s

Change in momentum = Final momentum - Initial momentum
= -1 - 2 = -3 kg·m/s

Magnitude of change in momentum = 3 kg·m/s

The student's logic is incorrect.

According to Newton’s Third Law of Motion, the action and reaction forces are equal and opposite, but they act on different objects, not on the same object. So, they do not cancel each other.
When you push the truck, the force you apply is on the truck, and the truck applies an equal and opposite force on you. These forces act on different bodies.
The truck does not move because the force you apply is not enough to overcome the friction between the truck’s tires and the ground, and the inertia of its large mass. If a much greater force is applied, the truck can move.