Motion in a plane (NCERT EXEMPLAR)

Q1: The angle between A = i + j and B = i - j is

• 45°
• 90°
• –45°
• 180°

Q2: Which one of the following statements is true?

• A scalar quantity is the one that is conserved in a process.
• A scalar quantity is the one that can never take negative values.
• A scalar quantity is the one that does not vary from one point to another in space.
• A scalar quantity has the same value for observers with different orientations of the axes.

Q3: The component of a vector r along X-axis will have maximum value if

• r is along positive Y-axis
• r is along positive X-axis
• r makes an angle of 45° with the X-axis
• r is along negative Y-axis

Q4: The horizontal range of a projectile fired at an angle of 15° is 50 m. If it is fired with the same speed at an angle of 45°, its range will be

• 60 m
• 71 m
• 100 m
• 141 m

Q5: Consider the quantities, pressure, power, energy, impulse, gravitational potential, electrical charge, temperature, area. Out of these, the only vector quantities are

• Impulse, pressure and area
• Impulse and area
• Area and gravitational potential
• Impulse and pressure

Q6: In a two dimensional motion, instantaneous speed v₀ is a positive constant. Then which of the following are necessarily true?

• The average velocity is not zero at any time.
• Average acceleration must always vanish.
• Displacements in equal time intervals are equal.
• Equal path lengths are traversed in equal intervals.

Q7: In a two dimensional motion, instantaneous speed v₀ is a positive constant. Then which of the following are necessarily true?

• The acceleration of the particle is zero.
• The acceleration of the particle is bounded.
• The acceleration of the particle is necessarily in the plane of motion.
• The particle must be undergoing a uniform circular motion

Q8: Three vectors A, B and C add up to zero. Find which is false.

• (A×B) × C is not zero unless B, C are parallel
• (A×B).C is not zero unless B, C are parallel
• If A, B, C define a plane, (A×B)×C is in that plane
• (A×B).C = |A||B||C| → C² = A² + B²

Q9: It is found that |A + B| = |A|. This necessarily implies,

• B = 0
• A, B are antiparallel
• A, B are perpendicular
• A.B ≤ 0

Q10: Two particles are projected in air with speed v₀ at angles θ₁ and θ₂ (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then tick the right choices

• angle of projection : θ₁ > θ₂
• time of flight : T₁ > T₂
• horizontal range : R₁ > R₂
• total energy : U₁ > U₂.

Q11: Following are four different relations about displacement, velocity and acceleration for the motion of a particle in general. Choose the incorrect one(s) :

• v_av = ½ [v(t₁) + v(t₂)]
• v_av = [r(t₂) - r(t₁)] / (t₂ - t₁)
• r(t₂) - r(t₁) = ½ [v(t₁) + v(t₂)] (t₂ - t₁)
• a_av = [v(t₂) - v(t₁)] / (t₂ - t₁)

Q12: For a particle performing uniform circular motion, choose the correct statement(s) from the following:

• Magnitude of particle velocity (speed) remains constant.
• Particle velocity remains directed perpendicular to radius vector.
• Direction of acceleration keeps changing as particle moves.
• Angular momentum is constant in magnitude but direction keeps changing.

Q13: For two vectors A and B, A + B = A - B is always true when

• A = 0 ≠ B
• A ⊥ B
• A ≠ 0 = B and A and B are parallel or anti parallel
• when either A or B is zero.