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Practice each question, then open the answer or worked solution.
Two particles are projected in air with speed v0, at angles θ1 and θ2 to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then tick the right choices
The correct answer is a) angle of project: q1 > q2 and b) time of flight: T1 > T2
A particle slides down a frictionless parabolic track starting from rest at point A. Point B is at the vertex of parabola and point C is at a height less than that of point A. After C, the particle moves freely in air as a projectile. If the particle reaches highest point at P, then
a) KE at P = KE at B
b) height at P = height at A
c) total energy at P = total energy at A
d) time of travel from A to B = time of travel from B to P
The correct answer is c) total energy at P = total energy at A
Following are four different relations about displacement, velocity, and acceleration for the motion of a particle in general. Choose the incorrect one (s):
The correct answer is a) vav = 1/2 [v(t1) + v(t2)] and c) r = 1/2 [v(t2)-v(t1)](t2-t1)
For a particle performing uniform circular motion, choose the correct statement from the following:
The correct answer is a) magnitude of particle velocity (speed) remains constant, b) particle velocity remains directed perpendicular to radius vector and c) direction of acceleration keeps changing as particle moves
For two vectors A and B,
is always true when
a)
b)
c)
and A and B are parallel or antiparallel
d) when either
is zero
The correct answer is b)
and d) when either
is zero
A cyclist starts from centre O of a circular park of radius 1 km and moves along the path OPRQO as shown in the figure. If he maintains constant speed of 10 m/s, what is his acceleration at point R in magnitude and direction?
The radius of the circular path is 1 km with O as the centre and at distance R.
Speed with which the cyclist is moving is 10 m/s.
Therefore, it can be said that the motion is uniform circular motion at R.
Therefore, R = 1000 m
v = 10 m/s
Therefore, acceleration, ac = v2/R = 0.1 m/s2 along RO.
A particle is projected in air at some angle to the horizontal, moves along parabola as shown in the figure, where x and y indicate horizontal and vertical directions respectively. Show in the diagram, direction of velocity and acceleration at points A, B, and C.
The projectile motion is either parabolic or part of it. The velocity is always tangential to the direction of velocities of A, B and C. At point B, the maximum height is reached by the trajectory. Therefore, the vertical component Bvy = 0 and horizontal component is u cos θ.
We know that the direction of acceleration is in the direction of force acting on the body. Therefore, here the direction of acceleration is in the direction of gravitational force and is always vertically downward which is equal to the acceleration due to gravity.
A ball is thrown from a roof top at an angle of 45o above the horizontal. It hits the ground a few seconds later. At what point during its motion, does the ball have
a) greatest speed
b) smallest speed
c) greatest acceleration?
Explain
a) Let us assume that the ball is projected from the point O at an angle 45o. From O to A there is an increase in the height of the ball such that the KE of the ball decreases. The height from point A to B decreases making the speed increase and now it is equal to the initial speed when the ball was at point O. This is because O and B are in the same horizontal line. From point B to C, again the speed increases as the height has reduced.
Therefore, the greatest speed is at C as vy maximum and vx = u/√2.
b) The smallest speed will be at point A as the height at this point is the highest and vy = 0 as the horizontal speed is the only constant value ie; u/√2
c) The greatest acceleration is acceleration due to gravity as only gravitational force is acting on the ball and in downward direction.
A football is kicked into the air vertically upwards. What is its
a) acceleration
b) velocity at the highest point
a) The acceleration of the football will be downward when it is kicked upwards as only gravitational force is acting on it.
b) The football will have its highest velocity when vy = 0.
A, B, and C are three non-collinear, non co-planar vectors. What can you say about direction of A(B×C)?
The direction of product of vectors B and C is perpendicular to the plane that contains vector B and C which is based on the Right hand grip rule.
The direction of vector A(B×C) is perpendicular to vector A and is in the plane which contains vectors B and C and is again based on the Right hand grip rule.
Short Answers