Assertion & Reason

Question 11 Mark

Assertion : The speedometer of an automobile measure the average speed of the automobile.
Reason : Average velocity is equal to total displacement per total time taken.

Answer

(e) Speedometer measures instantaneous speed of automobile.

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Question 21 Mark

Assertion : The average and instantaneous velocities have same value in a uniform motion.
Reason : In uniform motion, the velocity of an object increases uniformly.

Answer

(c) An object is said to be in uniform motion if itundergoesequaldisplacementinequalintervals of time.$\therefore v_{a v}=\frac{s_1+s_2+s_3+\ldots}{t_1+t_2+t_3+\ldots}=\frac{s+s+s\ldots}{t+t+t+\ldots}=\frac{n s}{n t}=\frac{s}{t}$and $v_{i n s}=\frac{s}{t}$.Thus, in uniform motion average and instantaneous velocities have same value andbodymoveswithconstantvelocity.

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Question 31 Mark

Assertion : The average speed of an object may be equal to arithmetic mean of individual speed.
Reason : Average speed is equal to total distance travelled per total time taken.

Answer

(b) Average speed $=$ Total distance $/$ Total time$\text { Time average speed }=\frac{v_1+v_2+v_3+\ldots \ldots}{n}$

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Question 41 Mark

Assertion : The position-time graph of a body moving uniformly is a straight line parallel to position-axis.
Reason : The slope of position-time graph in a uniform motion gives the velocity of an object.

Answer

(e) If the position-time graph of a body moving uniformly in a straightlineparalleltoposition axis, it means that the position of body is changing at constant time. The statement is abrupt and shows that the velocity of body is infinite.

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Question 51 Mark

Assertion : Displacement of a body is vector sum of the area under velocity-time graph.
Reason : Displacement is a vector quantity.

Answer

(a) According to definition,displacement $=$ velocity $\times$ time Since displacement is a vector quantity so its value is equal to the vector sum of the area undervelocitytimegraph.

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Question 61 Mark

Assertion : A body falling freely may do so with constant velocity.
Reason : The body falls freely, when acceleration of a body is equal to acceleration due to gravity.

Answer

(e) When a body falling freely, only gravitational force acts on it in vertically downward direction. Due to this downward acceleration the velocity of a body increasesandwillbemaximum when the body touches the ground.

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Question 71 Mark

Assertion : A body may be accelerated even when it is moving uniformly.
Reason : When direction of motion of the body is changing then body may have acceleration.

Answer

(e) The uniform motion of a body means that the body is moving with constant velocity, but if the direction of motion is changing (such as in uniform circular motion), its velocitychanges and thus acceleration is produced in uniform motion.

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Question 81 Mark

Assertion : Velocity-time graph for an object in uniform motion along a straight path is a straight line parallel to the time axis.
Reason : In uniform motion of an object velocity increases as the square of time elapsed.

Answer

(c) In uniform motion the object moves with uniform velocity, the magnitude of its velocity at different instant i.e. at $t=0, t=$ $1 \mathrm{sec}, t=2 \mathrm{sec}, \ldots$. will always be constant. Thus velocity-time graph for an object in uniform motion along a straight path is a straight line parallel to time axis.

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Question 91 Mark

Assertion : The displacement-time graph of a body moving with uniform acceleration is a straight line.
Reason : The displacement is proportional to time for uniformly accelerated motion.

Answer

(d) The displacement of a body moving in straight line is given by, $s=u t+\frac{1}{2at^2$. This is a equation of a parabola, not straight line. Therefore the displacement-time graph is a parabola. Thedisplacement time graph will be straight line, if acceleration of body is zero or body moving with uniform velocity.

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Question 101 Mark

Assertion : The relative velocity between any two bodies moving in opposite direction is equal to sum of the velocities of two bodies.
Reason : Sometimes relative velocity between two bodies is equal to difference in velocities of the two.

Answer

(b) When two bodies are moving in opposite direction, relative velocity between them is equal to sum of the velocity of bodies. But if the bodies are moving in same directiontheirrelative velocity is equal to difference in velocity of the bodies.

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Question 111 Mark

Assertion : A bus moving due north takes a turn and starts moving towards east with same speed. There will be no change in the velocity of bus.
Reason : Velocity is a vector-quantity.

Answer

(e) As velocity is a vector quantity, its value changes with change in direction. Therefore when a bus takes a turn from north to east its velocity will also change.

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Question 121 Mark

Assertion : The equation of motion can be applied only if acceleration is along the direction of velocity and is constant.
Reason : If the acceleration of a body is constant then its motion is known as uniform motion.

Answer

(d) Equation of motion can be applied if the acceleration is in opposite direction to that of velocity and uniform motion mean the acceleration is zero.

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Question 131 Mark

Assertion : Displacement of a body may be zero when distance travelled by it is not zero.
Reason : The displacement is the longest distance between initial and final position.

Answer

(c) The displacement is the shortest distance between initial and final position. When final position of a body coincides with its initial position, displacement is zero, but thedistance travelled is not zero.

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Question 141 Mark

Assertion : A body, whatever its motion is always at rest in a frame of reference which is fixed to the body itself.
Reason : The relative velocity of a body with respect to itself is zero.

Answer

(a) A body has no relative motion with respect to itself. Hence if a frame of reference of the body is fixed, then the body will be always at relative rest in this frame of reference.

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Question 151 Mark

Assertion : A body having non-zero acceleration can have a constant velocity.
Reason : Acceleration is the rate of change of velocity.

Answer

(e) As per definition, acceleration is the rate of change of velocity, i.e. $\vec{a}=\frac{d \vec{v}}{d t}$.If velocity is constant $d \vec{v} / d t=0, \therefore \vec{a=0$.Therefore, if a body has constant velocity it cannot have non zero acceleration.

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Question 161 Mark

Assertion : Distance-time graph of the motion of a body having uniformly accelerated motion is a straight line inclined to the time axis.
Reason : Distance travelled by a body having uniformly accelerated motion is directly proportional to the square of the time taken.

Answer

(e) For distance-time graph, a straight line inclined to time axis measures uniform speed for which acceleration is zero and for uniformly accelerated motion $S \propto t^2$.

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Question 171 Mark

Assertion : The slope of displacement-time graph of a body moving with high velocity is steeper than the slope of displacement-time graph of a body with low velocity.
Reason : Slope of displacement-time graph = Velocity of the body.

Answer

(a) Since slope of displacement-time graph measures velocity of an object.

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Question 181 Mark

Assertion : Position-time graph of a stationary object is a straight line parallel to time axis.
Reason : For a stationary object, position does not change with time.

Answer

(a) Position-time graph for a stationary object is a straightlineparalleltotimeaxishowingthat no change in position with time.

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Question 191 Mark

Assertion : The average speed of a body over a given interval of time is equal to the average velocity of the body in the same interval of time if a body moves in a straight line in one direction.
Reason : Because in this case distance travelled by a body is equal to the displacement of the body.

Answer

(a) When a body moves on a straight path in one direction value of \&displacementremains same so that average speed equals the average velocity for a given time interval.

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Question 201 Mark

Assertion : Rocket in flight is not an illustration of projectile.
Reason : Rocket takes flight due to combustion of fuel and does not move under the gravity effect alone.

Answer

(a) Motion of rocket is based on action reaction phenomena and is governedbyrateoffuelburning causing the change in momentum of ejected gas.

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Question 211 Mark

Assertion : When a body is subjected to a uniform acceleration, it always move in a straight line.
Reason : Straight line motion is the natural tendency of the body.

Answer

(e) It is not necessary that an object moving under uniform acceleration have straight path. eg. projectile motion.

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Question 221 Mark

Assertion : A negative acceleration of a body can be associated with a 'speeding up' of the body.
Reason : Increase in speed of a moving body is independent of its direction of motion.

Answer

(b) A body having negative acceleration can be associated with a speeding up, if object moves along negative $X$-direction with increasing speed.

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Question 231 Mark

Assertion : A positive acceleration of a body can be associated with a 'slowing down' of the body.
Reason : Acceleration is a vector quantity.

Answer

(b) A body having positive acceleration can be associated with slowing down, as time rate of change of velocity decreases, but velocity increases with time, from graph it is clear that slope with time axis decreases, but velocity increases with time.

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Question 241 Mark

Assertion : The position-time graph of a uniform motion in one dimension of a body can have negative slope.
Reason : When the speed of body decreases with time, the position-time graph of the moving body has negative slope.

Answer

(c) Negative slope of position time graph represents that the body ismovingtowardsthenegative direction and if the slope of the graph decrease with time then it represents the decrease in speed i.e. retardation in motion.

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Question 251 Mark

Assertion : The speed of a body can be negative.
Reason : If the body is moving in the opposite direction of positive motion, then its speed is negative.

Answer

(d) Speed can never be negative because it is a scalar quantity.

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Question 261 Mark

Assertion : An object can have constant speed but variable velocity.
Reason : Speed is a scalar but velocity is a vector quantity.

Answer

(a) Since velocity is a vector quantity, hence as its direction changes keeping magnitude constant, velocity is said to bechanged. But for constant speed in equal time interval distance travelled should be equal.

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Question 271 Mark

Assertion : The average velocity of the object over an interval of time is either smaller than or equal to the average speed of the object over the same interval.
Reason : Velocity is a vector quantity and speed is a scalar quantity.

Answer

(a) As displacement is either smaller or equal to distance but never be greater thandistance.

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Question 281 Mark

Assertion : If the displacement of the body is zero, the distance covered by it may not be zero.
Reason : Displacement is a vector quantity and distance is a scalar quantity.

Answer

(a) As distance being a scalar quantity is always positive but displacement being a vectormay be positive, zero and negative depending on situation.

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Question 291 Mark

Assertion : Two balls of different masses are thrown vertically upward with same speed. They will pass through their point of projection in the downward direction with the same speed.
Reason : The maximum height and downward velocity attained at the point of projection are independent of the mass of the ball.

Answer

(a) As motion is governed by force of gravity and acceleration duetogravity((g$isindependent of mass of object.

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Question 301 Mark

Assertion : A body can have acceleration even if its velocity is zero at a given instant of time.
Reason : A body is momentarily at rest when it reverses its direction of motion.

Answer

(a) When body going vertically upwards, reaches at the highest point, then it is momentarily at rest and it then reverses its direction. At the highest point of motion, its velocity is zero but its acceleration is equal to acceleration due to gravity.

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