Mechanics

The statement “friction force is a contact force while magnetic force is a non-contact force” is

[amp_mcq option1=”always true.” option2=”true only at 0°C.” option3=”a false statement.” option4=”either true or false depending upon the temperature of the surroundings.” correct=”option1″]

The statement “friction force is a contact force while magnetic force is a non-contact force” is always true.

Contact forces arise from the physical contact between objects (e.g., friction, normal force). Non-contact forces (also known as field forces) act between objects even when they are not in physical contact (e.g., gravitational force, magnetic force, electrostatic force). Friction requires surfaces to be in contact, while magnetic forces act through a magnetic field, regardless of contact.

This distinction between contact and non-contact forces is a fundamental concept in classical mechanics. Temperature or surrounding conditions do not alter the inherent nature of these forces in this classification.

In the given velocity (V) versus time (t) graph, accelerated and decelerated motions are respectively represented by line segments

[amp_mcq option1=”CD and BC” option2=”BC and AB” option3=”CD and AB” option4=”AB and CD” correct=”option3″]

In a velocity-time graph, accelerated motion is represented by a line segment with a positive slope (velocity increasing with time), and decelerated motion (or retardation) is represented by a line segment with a negative slope (velocity decreasing with time).

Line segment CD has a positive slope, indicating that velocity is increasing with time, which is accelerated motion. Line segment AB has a negative slope, indicating that velocity is decreasing with time, which is decelerated motion.

Line segment BC represents motion with constant velocity, meaning zero acceleration. The question asks for accelerated motion followed by decelerated motion, which corresponds to segments CD and AB respectively.

The figure shown above gives the time (t) versus position (x) graphs of three objects A, B and C. Which one of the following is the correct relation between their speeds $V_A$, $V_B$ and $V_C$, respectively at any instant (t > 0)?

[amp_mcq option1=”$V_A < V_B < V_C$" option2="$V_A > V_B > V_C$” option3=”$V_A = V_B = V_C \ne 0$” option4=”$V_A = V_B = V_C = 0$” correct=”option2″]

The speeds of the three objects are represented by the slope of their position-time graphs. The correct relation between their speeds is $V_A > V_B > V_C$.

– In a position-time (x-t) graph, the velocity (speed if motion is in one direction without change in direction) is given by the slope of the graph ($\Delta x / \Delta t$).
– A steeper slope indicates a higher speed, and a less steep slope indicates a lower speed.
– Examining the graph, the line for object A has the steepest slope.
– The line for object B has a slope less steep than A but steeper than C.
– The line for object C has the least steep slope.
– Since all slopes are positive, the objects are moving in the positive direction. The magnitude of the slope represents the speed.

All three graphs are straight lines, indicating that the objects are moving with constant velocities (uniform motion). If the lines were curved, the slope would change over time, indicating changing velocity (acceleration).

Suppose there are two planets, 1 and 2, having the same density but their radii are R₁ and R₂ respectively, where R₁ > R₂. The accelerations due to gravity on the surface of these planets are related as

[amp_mcq option1=”g₁ > g₂” option2=”g₁ < g₂" option3="g₁ = g₂" option4="Can't say anything" correct="option1"]

If two planets have the same density but different radii R₁ and R₂ with R₁ > R₂, the acceleration due to gravity on the surface of the planet with the larger radius (Planet 1) will be greater than that on the surface of the planet with the smaller radius (Planet 2), i.e., g₁ > g₂.

– The acceleration due to gravity on the surface of a sphere is given by g = GM/R², where G is the gravitational constant, M is the mass, and R is the radius.
– The mass M can be expressed as M = ρ * V, where ρ is the density and V is the volume. For a sphere, V = (4/3)πR³.
– Substituting this into the gravity formula: g = G * (ρ * (4/3)πR³) / R² = (4/3)πGρR.
– Since the density ρ and constants G, 4/3, and π are the same for both planets, the acceleration due to gravity is directly proportional to the radius (g ∝ R).
– Given R₁ > R₂, it follows that g₁ > g₂.

This relationship shows that for objects of the same density, larger objects exert stronger gravitational pull at their surface compared to smaller objects. This is because the increase in mass (proportional to R³) outpaces the increase in distance from the center (proportional to R²).

Which one of the following forces is non-central and non-conservative ?

[amp_mcq option1=”Frictional force” option2=”Electric force” option3=”Gravitational force” option4=”Mechanical force” correct=”option1″]

Frictional force is non-central and non-conservative.

A central force is one that acts along the line connecting the two interacting bodies or towards a fixed point. Gravitational and electrostatic forces between point masses/charges are examples of central forces. Frictional force acts parallel to the surfaces in contact, opposing relative motion, and is not necessarily directed along a line connecting centers or towards a fixed point, making it non-central.
A conservative force is one for which the work done in moving an object between two points is independent of the path taken. Work done by a conservative force over a closed loop is zero. Electric and gravitational forces are conservative. Frictional force dissipates energy as heat; the work done by friction depends on the path taken and is always negative (it opposes motion), meaning it is a non-conservative force.

Mechanical force is a very general term and can encompass various specific forces, some of which might be conservative (like elastic spring force) or non-conservative (like applied force doing work against friction). Therefore, ‘Mechanical force’ itself is not specific enough to be definitively classified as non-central and non-conservative; its nature depends on the specific force being considered.

The correct sequence of energy transfer that occurs when an apple falls to the ground is

[amp_mcq option1=”Gravitational potential energy $\to$ heat energy to air $\to$ kinetic energy $\to$ heat energy to ground and apple $\to$ sound energy” option2=”Gravitational potential energy $\to$ sound energy $\to$ heat energy to air $\to$ heat energy to ground and apple” option3=”Gravitational potential energy $\to$ kinetic energy $\to$ heat energy to air $\to$ heat energy to apple $\to$ sound energy” option4=”Gravitational potential energy $\to$ kinetic energy $\to$ sound energy $\to$ heat energy to air $\to$ heat energy to ground and apple” correct=”option3″]

The correct answer is C) Gravitational potential energy $\to$ kinetic energy $\to$ heat energy to air $\to$ heat energy to apple $\to$ sound energy.

When an apple falls, its initial gravitational potential energy is converted into kinetic energy. As the apple falls, air resistance acts on it, converting some of the kinetic energy into heat energy transferred to the surrounding air. Upon hitting the ground, the remaining kinetic energy is rapidly converted into sound energy (the impact sound) and heat energy due to the deformation and friction of the apple and the ground. Option C correctly shows the initial conversion from GPE to KE, followed by the dissipation of energy from KE into heat (to air and apple/ground) and sound upon impact. While heat to air occurs *during* the fall and sound/impact heat occurs *at the end*, option C provides the most plausible sequence among the choices, suggesting that the kinetic energy is the source from which heat to air, heat to apple, and sound energy arise.

Energy transformation during a fall is a classic example of the conservation of energy principle, where potential energy is converted into other forms. In realistic scenarios, dissipative forces like air resistance and the inelastic nature of collisions convert mechanical energy (potential and kinetic) into non-mechanical forms like heat and sound. The order in the options is not strictly temporal for the final dissipation forms, but C best represents the conversion path from potential to kinetic, and then the subsequent forms derived from kinetic energy.

Which one of the following is an example of the force of gravity of the earth acting on a vibrating pendulum bob ?

[amp_mcq option1=”Applied force” option2=”Frictional force” option3=”Restoring force” option4=”Virtual force” correct=”option3″]

When a pendulum bob is displaced from its equilibrium position, the force of gravity acting vertically downwards, combined with the tension in the string, results in a net force that pulls the bob back towards the equilibrium position. This force, which is always directed towards the equilibrium position and proportional to the displacement (for small angles), is known as the restoring force.

In simple harmonic motion, the restoring force is crucial as it is responsible for bringing the oscillating system back to its equilibrium state. For a simple pendulum, the component of gravity tangential to the arc of motion provides this restoring force.

Applied force is a general term for any external force. Frictional force opposes motion. Virtual force (or fictitious force) appears in non-inertial reference frames. Gravity itself is the fundamental force involved, but its component acting along the path of motion towards equilibrium is the restoring force in the context of oscillation.

Which of the following statements about a fluid at rest in a cup is/are correct ?

• 1. Pressure is same at all the points in the fluid.
• 2. Pressure is exerted on the walls.
• 3. Pressure exists everywhere in the fluid.

Select the correct answer using the code given below :

[amp_mcq option1=”1 and 2 only” option2=”2 and 3 only” option3=”1 only” option4=”1, 2 and 3″ correct=”option2″]

Statements 2 and 3 are correct regarding a fluid at rest in a cup. Statement 1 is incorrect as pressure varies with depth.

In a fluid at rest, pressure is exerted on any surface in contact with the fluid (like the walls of the cup) and acts perpendicular to the surface. Pressure also exists throughout the fluid’s volume. However, pressure in a fluid at rest varies with depth due to the weight of the fluid above, according to the formula P = P₀ + ρgh, where P₀ is the surface pressure, ρ is the fluid density, g is gravity, and h is depth. Thus, pressure is not the same at all points unless they are at the same depth.

Pressure in a fluid at rest is the same at all points at the same horizontal level. Pascal’s law states that pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel.

A ball balanced on a vertical rod is an example of

[amp_mcq option1=”stable equilibrium” option2=”unstable equilibrium” option3=”neutral equilibrium” option4=”perfect equilibrium” correct=”option2″]

A ball balanced precisely on a vertical rod is in unstable equilibrium.

– In unstable equilibrium, if the object is slightly displaced from its equilibrium position, it will move further away from that position.
– A ball balanced on a pointed object or the crest of a curve represents a point of unstable equilibrium. Any tiny disturbance will cause it to fall.

– Stable equilibrium occurs when a slight displacement causes the object to return to its original position (e.g., a ball in the bottom of a bowl).
– Neutral equilibrium occurs when a slight displacement causes the object to remain in its new position (e.g., a ball on a flat surface).

Which one of the following statements about the mass of a body is correct ?

[amp_mcq option1=”It changes from one place to another” option2=”It is same everywhere” option3=”It depends on its shape” option4=”It does not depend on its temperature” correct=”option2″]

Statement B is correct. Mass is a fundamental property of a body that represents the amount of matter it contains. It is an intrinsic property and remains the same regardless of the body’s location (where gravity varies) or its shape.

– Mass is distinct from weight, which is the force of gravity acting on a mass and therefore changes with location.
– Mass is invariant under changes in location, shape, or phase (in a classical context).

Statement A is incorrect as it describes weight, not mass. Statement C is incorrect; mass depends on the amount of matter, not its arrangement (shape). Statement D is also correct in a classical physics context, as temperature changes (which represent changes in internal energy) cause only negligible changes in mass according to E=mc^2, which are typically ignored unless dealing with nuclear reactions or extremely high energies. However, B is a more fundamental and universally applicable definition when comparing mass to variables like location. Since only one option can be chosen, B is the most definitive correct statement about mass.