| # | Statement (Answer in bold) |
|---|---|
| 1 | To produce acceleration or a change in the state of motion, force is required |
| 2 | Passengers lean forward when sudden brake is applied in a moving vehicle. This can be explained by inertia of motion |
| 3 | By convention, the clockwise moments are taken as negative and the anticlockwise moments are taken as positive |
| 4 | Gears are used to change the speed and torque of rotation in a car. |
| 5 | A man of mass 100 kg has a weight of 980 N at the surface of the Earth |
| # | Statement | Answer | Correction (if False) |
|---|---|---|---|
| 1 | The linear momentum of a system of particles is always conserved. | False | In the absence of external force, the linear momentum of a system of particle is always conserved. |
| 2 | Apparent weight of a person is always equal to his actual weight | False | Both apparent weight and actual weight can be greater or lesser according to the movement of the person inside the lift. |
| 3 | Weight of a body is greater at the equator and less at the polar region. | False | Weight of the body is less at equator, more at polar region. |
| 4 | Turning a nut with a spanner having a short handle is so easy than one with a long handle. | False | Formula: torque = F x d (torque in N m). Example: Apply F = 10 N. Short handle d_short = 0.05 m -> torque_short = 10 x 0.05 = 0.5 N m. Long handle d_long = 0.20 m -> torque_long = 10 x 0.20 = 2.0 N m. To get torque = 2.0 N m with the short handle requires F = torque/d_short = 2.0/0.05 = 40 N. Hence the long handle needs much less force to produce the same turning effect. |
| 5 | There is no gravity in the orbiting space station around the Earth. So the astronauts feel weightlessness. | False | When space station and astronauts have equal acceleration, they are under free fall condition, so both astronaut and space station are in the state of weightlessness. |
| Column A | Column B |
|---|---|
| Newton's law | Match entry for 'Newton's law' should read: 'Newton's First Law - Law of Inertia: A body remains at rest or moves with constant velocity in a straight line unless acted upon by a net external force.' If the match required a single word, use 'Inertia' or the phrase 'law of inertia.' |
| Newton's II law | Correct statement: The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction of the force. Formula: F = dp/dt. For constant mass, dp/dt = m dv/dt = ma, so F = ma. Units: Force (F) in newtons (N); 1 N = 1 kg m/s2. Quick example: A 2 kg object accelerating at 3 m/s2 experiences F = ma = 2x3 = 6 N. |
| Newton's III law | For every action force, there is an equal and opposite reaction force. These two forces act on two different bodies. |
| Law of conservation of linear momentum | If no external net force acts on a system, the total linear momentum of the system remains constant. |
2) At depth d: g(d) = g0(1 - d/R) => g decreases with depth.
3) Therefore Assertion is true. The Reason is false because g is independent of the mass of the object; correct dependence is on Earth's mass M and radial distance r.
Inertia is the inherent property of an object that resists any change in its state of rest or uniform motion along a straight line, unless acted upon by an external unbalanced force. This means an object at rest will stay at rest, and an object in motion will continue in motion with the same velocity, unless a net force intervenes. Inertia is directly proportional to the mass of the object; a more massive object has more inertia. It is classified into three types: inertia of rest, which is the resistance to a change in the state of rest; inertia of motion, which is the resistance to a change in the state of uniform motion; and inertia of direction, which is the resistance to a change in the direction of motion. Mass is the quantitative measure of inertia, and its SI unit is the kilogram (kg).
Forces can be classified into two main types based on whether they require physical contact between the interacting bodies or not. The first type is contact force, which is a force that acts only when two bodies are in direct physical contact. Examples of contact forces include frictional force, which opposes motion between surfaces in contact; normal force, which is perpendicular to the surface of contact; and muscular force, which is applied by the muscles of living beings. The second type is non-contact force, also known as action-at-a-distance force, which acts without any physical contact between the bodies. Examples of non-contact forces include gravitational force, the attractive force between any two objects with mass; magnetic force, exerted by magnets on other magnetic materials; and electrostatic force, which is the force between charged objects.
Mass is defined as the quantity of matter contained within a body. It is a fundamental property of matter and is independent of external conditions such as temperature, pressure, or location. The SI unit for mass is the kilogram (kg). Mass is typically measured using a physical balance, which compares the unknown mass to known standard masses, or an electronic balance, which uses a load cell to measure the force exerted by the mass and converts it into a mass reading. A larger mass indicates a greater amount of matter.
Mass is a scalar quantity because it is defined solely by its magnitude and does not possess any direction. It represents the amount of matter present in a body. Unlike vector quantities, which require both magnitude and direction for their complete description, mass only needs a numerical value and a unit. The SI unit of mass is the kilogram (kg). Being a scalar quantity, mass can be added or subtracted using simple arithmetic rules, making calculations involving mass straightforward.
The quantity described is mass. Its SI unit is the kilogram (kg), which is the base unit of mass in the International System of Units. The kilogram is a measure of the amount of matter in an object and is a fundamental property that remains constant regardless of the object's location or the gravitational field it is in. While other units like grams (g) or milligrams (mg) are used for smaller quantities, the kilogram is the standard unit for scientific and everyday measurements.
True. The mass of a body remains constant at any point on Earth, and indeed, anywhere in the universe. This is because mass is defined as the amount of matter contained within an object, and this amount does not change with location. While the weight of an object, which is the force of gravity acting on its mass (Weight = mass × acceleration due to gravity, W=mg), can vary because the acceleration due to gravity (g) changes slightly from place to place on Earth due to factors like altitude and latitude, the mass itself remains invariant.
True. Mass can be accurately measured using a physical balance, also known as a beam balance. This instrument works on the principle of moments and compares the unknown mass placed on one pan with known standard masses placed on the other pan. When the beam is balanced, the unknown mass is equal to the sum of the standard masses used. The SI unit for mass is the kilogram (kg), and physical balances are a common and reliable method for determining this fundamental property of matter.
2) Impulse magnitude = |Delta p| = m v (units kg m/s or N s).
3) J = F_avg Delta t => F_avg = Delta p/Delta t. Increasing Delta t (by pulling hands back) decreases F_avg.
Units: momentum (kg m/s), impulse (N s), force (N).
2. Apparent weight = normal reaction R = m(g - a).
3. For free fall/orbit a = g -> R = m(g - g) = 0.
4. With R = 0 there is no contact force to hold the astronaut to any surface, so the astronaut floats (appears weightless).
Choose sign convention: take initial velocity toward floor as -10 m s^-1 and final after rebound as +10 m s^-1.
p_initial = m u = 1 x (-10) = -10 kg m s^-1
p_final = m v = 1 x (+10) = +10 kg m s^-1
Delta p = p_final - p_initial = 10 - (-10) = 20 kg m s^-1
Therefore change in linear momentum = 20 kg m s^-1 (directed opposite to the initial velocity).
Therefore g1/g2 = (M1/M2) * (R2^2/R1^2)
= (2/3) * (7^2/4^2)
= (2/3) * (49/16)
= 98/48 = 49/24
Thus g1 : g2 = 49 : 24.
(ii) Inertia of motion: The resistance of a body to change its state of motion. Example: An athlete runs before jumping-the forward motion helps the athlete travel a longer distance in the jump.
(iii) Inertia of direction: The resistance of a body to change its direction of motion. Example: When a car makes a sharp turn, passengers tend to be thrown outward or lean sideways because their bodies tend to continue in the original straight-line motion.
(ii) Newton's second law: The force acting on a body is equal to the rate of change of its momentum. For constant mass, F = ma.
(iii) Newton's third law: For every action, there is an equal and opposite reaction. Action and reaction always act on two different bodies.
2. Change in momentum Delta p = Pf - Pi = m(v - u).
3. Rate of change of momentum = Delta p/Delta t = m(v - u)/t.
4. By Newton's second law, net force F = rate of change of momentum, so F = m(v - u)/t.
5. Define acceleration a = (v - u)/t. Therefore F = m a.
6. In differential form (general form): F = dp/dt. If mass is constant, dp/dt = m dv/dt = m a.
7. SI unit: force F in newtons (N); 1 N = 1 kg m s^-2.
Rocket propulsion is a fascinating application of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction, and the law of conservation of linear momentum. In a rocket, fuel and an oxidizer are mixed and burned in a combustion chamber, producing a large volume of hot, high-pressure gases. These gases are then expelled at extremely high velocity through a specially shaped nozzle at the rear of the rocket. This expulsion of gases backward creates a forward thrust, which is an equal and opposite reaction force that propels the rocket. As the rocket expels mass (the exhaust gases) backward, it gains forward momentum. Since the total momentum of the system must be conserved, the rocket moves forward. The rate at which the fuel is consumed and expelled means the rocket's mass continuously decreases, and according to the principles of motion, its velocity increases significantly as it ascends.
Let two bodies of masses m1 and m2 be separated by distance r. Then F is proportional to m1 x m2 and F is proportional to 1/r^2. Therefore, F is proportional to (m1 x m2)/r^2. Introducing the universal gravitational constant G, we get F = Gm1m2/r^2. The SI unit of G is N m^2 kg^-2 and its value is 6.674 x 10^-11 N m^2 kg^-2.
The universal law of gravitation, formulated by Sir Isaac Newton, has profound applications in understanding the cosmos and celestial mechanics. Firstly, it is instrumental in determining the masses of celestial bodies like the Earth, the Moon, the Sun, and other planets by observing their gravitational effects on other objects. Secondly, it allows us to accurately calculate the acceleration due to gravity (g) at different points on Earth's surface and understand how it varies with altitude and depth. Thirdly, the law provides a fundamental explanation for the motion of planets around the Sun and the motion of natural satellites (like the Moon) and artificial satellites around planets, describing their elliptical orbits. Fourthly, it enables scientists to predict the paths and orbits of comets, asteroids, and other astronomical bodies, which is crucial for space exploration and hazard assessment. Fifthly, it explains the phenomenon of tides on Earth, which are primarily caused by the differential gravitational pull of the Moon and, to a lesser extent, the Sun on Earth's oceans. Finally, the universal law of gravitation is used in astrophysics to study binary star systems and to detect the presence of exoplanets by observing the subtle wobble or disturbance in the motion of nearby stars caused by the gravitational influence of an unseen orbiting planet.
2. Acceleration a = F_applied / m_total = 15 N / 10.0 kg = 1.5 m/s2.
3. Contact force on 2 kg block F_contact = m2 x a = 2.0 kg x 1.5 m/s2 = 3.0 N.
(Answer: 3 N towards the direction of the applied force.)
Momentum: p_t = m_t v_t = 4m x (v_b/2) = 2 m v_b. p_b = m v_b. Therefore p_t : p_b = 2m v_b : 1m v_b = 2 : 1.
(Units of momentum: kg m/s.)
2) Describe the hazard: In a sudden stop or collision passenger's velocity v must change to zero (Delta v = -v); momentum change Delta p = mDelta v.
3) Use formula: average stopping force F_avg = mDelta v/Delta t. For fixed m and Delta v, larger Delta t -> smaller F_avg.
4) Apply to helmet: helmet cushions impact, increases Delta t and impact distance, so F_avg on skull decreases -> less injury.
5) Apply to seat belt: seat belt applies the unbalanced force to decelerate passenger, increases effective Delta t and spreads force across torso, preventing ejection and reducing localized injuries.
6) Units reminder: mass (kg), velocity (m/s), force (N = kg m/s2), impulse (N s). Example (optional): A 70 kg person at 20 m/s (72 km/h) stopped in 0.05 s -> F_avg approx. 70x20/0.05 = 28,000 N; if stopping time increases to 0.5 s with restraint/cushioning -> F_avg approx. 2,800 N, a tenfold reduction in average force.
Study Smarter, Score Higher.
Revise this Samacheer Class 10 Science topic, then continue with the Revision Challenge.