Q.1 The center of mass of a system of two equal masses placed at the ends of a uniform rod lies at:
At the midpoint of the rod
Closer to one mass
At the end of the rod
Outside the rod
Explanation - For equal masses symmetrically placed, the center of mass lies exactly at the midpoint of the system.
Correct answer is: At the midpoint of the rod
Q.2 If a constant force acts on a system, the velocity of the center of mass:
Remains zero
Changes linearly with time
Becomes infinite
Oscillates
Explanation - A constant force produces uniform acceleration, so the velocity of the center of mass changes linearly with time.
Correct answer is: Changes linearly with time
Q.3 The center of mass of Earth-Moon system lies:
At the center of Earth
At the center of Moon
Between Earth and Moon, closer to Earth
Outside both Earth and Moon
Explanation - Since Earth is much heavier, the center of mass lies closer to Earth on the line joining Earth and Moon.
Correct answer is: Between Earth and Moon, closer to Earth
Q.4 In the absence of external forces, the linear momentum of a system:
Increases
Decreases
Remains conserved
Oscillates
Explanation - Conservation of momentum states that in the absence of external forces, total momentum of a system remains constant.
Correct answer is: Remains conserved
Q.5 Two balls collide elastically. Which of the following is conserved?
Momentum only
Kinetic energy only
Both momentum and kinetic energy
Neither momentum nor kinetic energy
Explanation - In elastic collisions, both momentum and kinetic energy are conserved.
Correct answer is: Both momentum and kinetic energy
Q.6 The center of mass of a system of particles depends on:
Only masses
Only positions
Both masses and positions
Neither masses nor positions
Explanation - The center of mass is the weighted average of positions, weighted by their respective masses.
Correct answer is: Both masses and positions
Q.7 If two particles of unequal masses collide elastically, the velocity of the center of mass after collision:
Increases
Decreases
Remains same
Becomes zero
Explanation - The velocity of the center of mass depends only on total momentum and total mass, both of which are conserved in collisions.
Correct answer is: Remains same
Q.8 A system of two equal masses connected by a massless rod rotates about its center of mass. The center of mass moves:
In a straight line
In a circle
Remains at rest
Accelerates
Explanation - When no external force acts, the center of mass remains at rest even though the masses rotate.
Correct answer is: Remains at rest
Q.9 In rocket propulsion, the principle involved is:
Conservation of energy
Conservation of angular momentum
Conservation of linear momentum
Newton's first law
Explanation - Rocket propulsion works on the principle of conservation of momentum as expelled gases provide thrust in opposite direction.
Correct answer is: Conservation of linear momentum
Q.10 The center of mass of a system moves as if:
All internal forces act on it
All mass is concentrated there and all external forces act on it
It has infinite mass
It is unaffected by any forces
Explanation - The motion of the center of mass can be described as if the whole mass is concentrated at the center and all external forces act on it.
Correct answer is: All mass is concentrated there and all external forces act on it
Q.11 In an isolated system, the position of the center of mass:
Remains fixed
Changes randomly
Oscillates
Depends on internal forces
Explanation - Internal forces cannot move the center of mass; only external forces can shift it.
Correct answer is: Remains fixed
Q.12 When a bullet is fired from a gun, the gun recoils because of:
Conservation of energy
Newton’s first law
Conservation of momentum
Gravity
Explanation - The bullet gains forward momentum and the gun gains backward momentum so that total momentum is conserved.
Correct answer is: Conservation of momentum
Q.13 If two particles move towards each other and collide perfectly inelastically, their final velocity of the center of mass is:
Zero
Equal to initial velocity of heavier mass
Equal to initial velocity of lighter mass
Equal to velocity of the center of mass before collision
Explanation - Center of mass velocity is unaffected by internal interactions and remains the same before and after collision.
Correct answer is: Equal to velocity of the center of mass before collision
Q.14 The center of mass of a uniform semicircular ring lies:
At the center of the circle
At the midpoint of the arc
On the axis perpendicular to the diameter
At one end of the diameter
Explanation - The symmetry of the ring places the center of mass on the perpendicular bisector of the diameter at a specific distance from the center.
Correct answer is: On the axis perpendicular to the diameter
Q.15 In a collision between two particles, the total momentum of the system:
Always conserved
Never conserved
Conserved only in elastic collisions
Conserved only in inelastic collisions
Explanation - Momentum conservation is universal, independent of the type of collision, provided no external force acts.
Correct answer is: Always conserved
Q.16 The motion of the center of mass of a system under no external force is:
Uniform motion in a straight line
Accelerated motion
Circular motion
Oscillatory motion
Explanation - In absence of external force, the center of mass moves with constant velocity.
Correct answer is: Uniform motion in a straight line
Q.17 The kinetic energy of the center of mass of a system depends on:
Relative motion of particles
Velocity of center of mass
Internal forces only
Mass distribution only
Explanation - The kinetic energy of translation of the system is due to the motion of the center of mass with velocity v_CM.
Correct answer is: Velocity of center of mass
Q.18 When a bomb explodes in mid-air, the center of mass of its fragments:
Follows a parabolic path
Stops
Moves randomly
Accelerates vertically
Explanation - Despite the explosion, the center of mass follows the trajectory dictated by gravity, which is parabolic.
Correct answer is: Follows a parabolic path
Q.19 The center of mass of a uniform triangular lamina is located at:
Midpoint of base
Intersection of medians
Centroid of the base
One corner of the triangle
Explanation - The centroid of a triangle (intersection of medians) is its center of mass.
Correct answer is: Intersection of medians
Q.20 In an elastic head-on collision between two equal masses, one at rest, the moving mass after collision:
Comes to rest
Continues with same velocity
Moves in opposite direction
Splits into two parts
Explanation - In elastic collisions of equal masses, the moving mass comes to rest and transfers velocity to the other mass.
Correct answer is: Comes to rest
Q.21 The center of mass of a uniform rod of length L lies at:
One end
L/4 from one end
L/2 from one end
Outside the rod
Explanation - For a uniform rod, the center of mass is at its midpoint.
Correct answer is: L/2 from one end
Q.22 Momentum is a:
Scalar
Vector
Dimensionless quantity
Pseudo-vector
Explanation - Momentum has both magnitude and direction; it is a vector quantity.
Correct answer is: Vector
Q.23 In a two-body system, internal forces:
Can change total momentum
Cannot change total momentum
Always increase total momentum
Always decrease total momentum
Explanation - Internal forces cancel in pairs due to Newton's third law and hence cannot change the system’s momentum.
Correct answer is: Cannot change total momentum
Q.24 Impulse imparted to a system is equal to:
Change in velocity
Change in force
Change in momentum
Change in energy
Explanation - Impulse is defined as the product of force and time, which equals the change in momentum of the system.
Correct answer is: Change in momentum
Q.25 The center of mass of two particles of masses m and 2m separated by distance d lies:
At midpoint of d
Closer to m
Closer to 2m
At distance d from 2m
Explanation - The center of mass lies nearer to the heavier mass in proportion to their masses.
Correct answer is: Closer to 2m