KINEMATICS
1 DPP – 5
1.
Two small balls of same size and different masses m1 and m2 (m1 > m2) are tied by a thin weightless thread and dropped from a balloon. The force of air on one ball during the flight after the motion of the balls has become steady will be (a) m1 m 2 g
2.
(b)
m1 m2 2
g
(c) m1 m2 g
(d)
m1 m2 2
g
Velocity and acceleration of a particle at some instant of time are v ( 2iˆ ˆj 2kˆ ) m/s and a (iˆ 6 ˆj kˆ) m/s2. Then, the speed of the particle is
(a) increasing at the rate of 2 m/s2 (c) increasing at the rate of 4 m/s2
(b) decreasing at the rate of 2 m/s2 (d) decreasing at the rate of 4 m/s2
3.
The velocity of a particle moving on the x-axis is given by v = x2 + x where v is in m/s and x is in m. Its acceleration in m/s2 when passing through the point x = 2m is (a) 0 (b) 5 (c) 11 (d) 30
4.
A particle starts moving rectilinearly at time t = 0 such that its velocity v changes with time t according to the equation v = t2 – t where t is in seconds and v is in m/s. The time interval for which the particle retards is (a) t < 1/2 (b) 1/2 < t < 1 (c) t > 1 (d) t < 1/2 and t > 1
5.
t 2 2 cos kˆ ms–2. The acceleration of a particle is given by a 2iˆ 6tˆj 9 3 At t = 0, r = 0 and v ( 2iˆ ˆj ) m/s. The position vector at t = 2 s will be (a) 8iˆ 10 ˆj kˆ m (b) 8iˆ 10 ˆj 3kˆ m
(c) 3iˆ 8 ˆj 10kˆ m
(d) 10iˆ 3 ˆj 8kˆ m
6.
A train of length l = 350 m starts moving rectilinearly with constant acceleration a = 3 × 10–2 m/s2. After 30 s the headlight of the train is switched on (event 1). After 60s from this event the tail signal light is switched on (event 2). Find the distance (in m) between these events in the reference frames fixed to the earth.
7.
A particle moves in a straight line with an acceleration (12 s2) ms–2 where s is the displacement of the particle in metre from O, a fixed point on the line, at time t seconds. The particle has zero velocity when its displacement from O is –2m. Find the velocity (in m/s) of the particle as it passes through O.
8.
A ball is projected on a smooth inclined plane in a direction perpendicular to line of greatest slope with velocity of 8m/s. Find it’s speed (in m/s) after 1 sec.
8m/s
37°
KINEMATICS
2 DPP – 6
2.
In the figure a block of mass M is at rest on the floor. The acceleration with which should a boy of mass m climb along the rope of negligible mass, so as to just lift the block from the floor is M (a) equal to 1 g m
M (b) greater than 1 g m
M (c) equal to g m
M (d) greater than g m
B a m M
Velocity-time graph of a particle is in the shape of a semicircle of radius R as shown in figure. Its average acceleration from T = 0 to T = R is: (a) 0 m/s2 (b) 1 m/s2 (c) R m/s2 (d) 2R m/s2
Velocity (m/s)
1.
R
(0, 0) (R, 0) Time(s)
3.
Two cars initially at rest start a race. Car A accelerates at constant rate a, while car B moves with zero initial acceleration such that rate of change of acceleration is constant. At t = 1 s both the cars are at same position. Then at t = 0.5 s (a) car A is ahead (b) car B is ahead (c) both are at same positions (d) data insufficient
4.
Each of the three graphs represents acceleration versus time for an object that has a positive velocity at time t1. Graphs showing the object with increasing speed in the interval t1 to t2 are a a a
I
t1
III
II
t2
t
(a) graph I, only (c) graphs I and III, only
t1
t2
t
t1
t2
t
(b) graphs I and II, only (d) graphs I, II, and III
KINEMATICS
5.
3
The displacement s travelled by a body in time t is given by s constants. The acceleration of the body is s 2a (a) 3 2b (b) 2 t 2t
(c) 2b
2a t3
a bt 2 , where a and b are t
(d)
s t2
6.
An automobile passes a stationary policeman who is hiding behind a bill board with a motorcycle. After a 2.0 sec delay (reaction time) the policeman accelerates to his maximum speed of 150 km/hr in 12 sec and catches the automobile 1.5 km beyond the billboard. Find the speed of automobile (in m/s).
7.
A passenger reaches the platform and finds that the second last boggy of the train is passing him. The second last boggy takes 3s to pass the passenger, and the last boggy takes 2s to pass him. How late in the milliseconds is the passenger for the departure of the train? Assume that the train accelerates at constant rate and all the boggies are of equal length.
8.
A motorboat going downstream overcome a bottle floating in river at a point A. After 60 minutes, it turned back and after some time passed the bottle at a distance 6.0 km from the point A. Find the flow velocity (in km/h) assuming the duty of the engine to be constant.
KINEMATICS
4 DPP – 7
1.
Two identical particles A and B, each of mass m, are interconnected by a spring of stiffness k. If the particle B experiences a force F and the elongation of the spring is x, the relative acceleration between the particles is equal to (a)
F 2m
(b)
F kx m
(c)
F 2kx m
(d)
kx m
2.
The slope of the velocity displacement graph of a particle moving along a straight line is 10 unit at a position where velocity is 5 unit. The acceleration of the particle at that position is (a) 50 unit (b) 5 unit (c) 10 unit (d) 2 unit
3.
Choose the incorrect statement (a) Average speed of a particle in a given time is never less than the magnitude of the average velocity. d dv (b) It is possible to have a situation in which 0 but v 0. dt dt (c) The average velocity of a particle is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval. (d) The average velocity of a particle moving on a straight line is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval. (Infinite accelerations are not allowed).
4.
A man standing on the edge of the terrace of a high rise building throws a stone vertically up with a speed of 20 m/s. Two seconds later an identical stone is thrown vertically down with the same speed. Then, choose the incorrect option (a) the relative velocity between the two stones remain constant till one hits the ground. (b) both will have the same kinetic energy when they hit the ground. (c) the time interval between their hitting the ground is 4 seconds. (d) if the collisions on the ground are perfectly elastic both will rise to the same height above the ground.
5.
An object is moving along the x axis with position as a function of time given by x = x(t). Point O is at x = 0. The object is definitely moving towards O when (a) dx/dt < 0 (b) dx/dt > 0 (c) d(x2) / dt < 0 (d) d(x2)/dt > 0
6.
At a distance of 400m from the traffic light brakes are applied to a car moving with velocity of 54 km/hr. Determine the distance of the car (in m) relative to the traffic light 1 minute after the application of the brakes if its acceleration is –0.3m/s2.
7.
Two particles are moving along two long straight lines, in the same plane, with the same speed = 20 cm/s. The angle between the two lines is 60°, and their intersection point is O. At a certain moment, the two particles are located at distances 3m and 4m from O, and are
KINEMATICS
5
moving towards O. Find the shortest distance (in mm) between them subsequently. ( 3 =1.73) 8.
The position of a particle moving along a straight line is given by x = 3sint, where t is in s 1 3 and x is in m. Find the distance (in cm) travelled by the particle from t = s to t = s. 4 4 2 1.414
KINEMATICS
6 DPP – 8
1.
A body of mass m is released from the top of a inclined plane of length l from height h. If the resistive force is f, then the velocity of the body at the bottom in ms–1 will be (a)
2 mgh f l m
(b) 2 gh f / l
(c)
2 gh m
(d) zero
2.
A train carriage moves along the X-axis with a uniform acceleration. An observer A in the train sets a ball in motion on frictionless floor of the carriage with a velocity relative to the carriage. The direction of ball makes an angle with the X-axis. Let B be an observer standing on the ground outside the train. The subsequent path of the ball will be (a) a straight line with respect to observer A (b) parabolic with respect to observer B (c) parabolic with respect to observer A (d) none of these
3.
A car with a vertical wind shield moves along in a rain storm at the speed of 40 km/hr. The rain drops fall vertically with a terminal speed of 20 m/s. The angle with the vertical at which the rain drop strike the wind shield is (a) tan–1 (5/9) (b) tan–1 (9/5) (c) tan–1 (3/2) (d) tan–1 (3)
4.
A particle of mass m moves on the x-axis under the influence of a force of attraction k towards the origin O given by F 2 iˆ . If the particle starts from rest at x = a, the speed it x will attain to reach at distance x from the origin O will be 1
(a)
2k x a 2 m ax
1
(b)
2k x k 2 m ax
(c)
k ax m x a
1
(d)
m a x 2 2k ax
5.
Point A moves uniformly with velocity 5 m/s so that its velocity vector is continually ‘aimed’ at point B which in its turn moves rectilinearly and uniformly with velocity 3 m/s. At the initial moment of time their velocities are perpendicular and the points are separated by a distance of 32 m. Find the time (in second) after which particles will meet.
6.
A particle is released from a height of H = 400 m. Due to the wind the particle gathers the horizontal velocity v x ay where a 5 sec–1 and y is the vertical displacement of the particle from point of release. Find the horizontal drift (in m) of the particle when it strikes the ground.
7.
Rain is falling vertically with a speed of 20 ms-1 relative to air. A person is running in the rain with a velocity of 5 ms-1 and a wind is also blowing with a speed of 15 ms–1 (both towards east). Find the cotangent of the angle with the vertical at which the person should hold his umbrella so that he may not get drenched.
8.
A glass wind screen whose inclination with the vertical can be changed is mounted on a car. The car moves horizontally with a speed of 2m/s. If the angle of the wind screen with vertical is when vertically downward falling raindrops with velocity of 6 m/s strikes the screen perpendicularly. Find tan .
KINEMATICS
1.
7
DPP – 9 As shown in the figure, two blocks of masses 3 kg and 6 kg are connected by a string of mass 1 kg and placed on a frictionless surface. The system is pulled from the side of block 3 kg with a constant force 20 N. Tension in the string at points A, B and C is (a) 16 N, 14 N, 12 N (c) 14 N, 12 N, 10 N
20N
3kg
6kg
1kg B
A
C
(b) 14 N, zero, 12 N (d) 14 N, 13 N, 12 N
2.
The velocities in x and y direction of a particle moving in xy plane is given by v x a0 t ; v y x where a 0 and are some constants, t is time and x is the displacement in x direction at any time t. The trajectory of the particle will be 92 2 92 22 2 22 3 (a) y 3 x (b) y 3 x (c) y 2 2 x 2 (d) y 2 x 9a 0 9a 0 2a0 2a0
3.
Three particles A, B and C are thrown simultaneously with speeds v A , v B and vC with A horizontally, B at an angle of 60° with the horizontal and C vertically in such a manner that they collide simultaneously at H, the highest point of the parabolic path of B. If the acceleration due to gravity is g, then the ratio of the speeds v A : v B : vC is (a) 1 : 1 : 1
4.
5.
(b) 1 : 2 : 3
(c) 3 : 1 : 1
A golfer standing on level ground hits a ball with a velocity of u = 52 m/s at an angle above the horizontal. If tan = 5/12, then the time for which the ball is at least 15m above the ground (i.e. between A and B) will be (take g = 10 m/s2) (a) 1 sec (b) 2 sec (c) 3 sec
vA
A
H vB
60° C
B
(d) 3 : 2 : 1
uA 15 m
B 15 m
(d) 4 sec
Two boats were going down stream with different velocities. When one overtook the other, a plastic ball was dropped from one of the boats. Some time later both boats turned back simultaneously & went at the same speeds as before (relative to the water) towards the spot where the ball had been dropped. The boat reaching earlier to the ball will be (a) the boat which has greater velocity (relative to water) (b) the boat which has lesser velocity (relative to water) (c) both will reach the ball simultaneously (d) cannot be decided unless we know the actual values of the velocities and the time after which they turned around.
KINEMATICS
8
6.
A boy throws a ball upwards with a velocity 12 m/sec at a angle with the vertical. The wind imparts a horizontal acceleration of 0.4 m/s2. If for angle the ball thrown returns to the point of release, then find cot .
7.
A man can throw a stone with a speed of 10 m/s. The maximum horizontal distance to which he can throw the stone in a room of height 2m is x . Find the value of x,
8.
To a man running upwards on the hill, the rain appears to fall vertically downwards with 4m/s. The velocity vector of the man with respect to earth is ( 2iˆ 3 ˆj ) m/s. If the man starts running down the hill with the same speed, the relative speed of the rain with respect to man is n m/s. Find the value of n.
KINEMATICS
9 DPP – 10
1.
To measure the acceleration of a vertically upward moving elevator, a small body weighing 3 N is fastened to one end of a massless string which is in turn attached to the top of the elevator. If the tension in the string is 5N, then the acceleration of the elevator is (a)
2.
3.
4.
5 9.8 m/s 2 3
(b)
3 9.8 m/s 2 5
(c) 0 m/s2
(d)
2 9.8 m/s 2 3
A particle moves in the x-y plane with velocity v k1iˆ k 2 xˆj, where iˆ and ˆj are the unit vectors along the x and y axes and k1 and k 2 are constants. At the initial moment, the particle was located at the point x = y = 0. The equation to the particle’s trajectory is k k 2k 2k (b) y 2 x 2 (c) y 1 x 2 (d) y 2 x 2 (a) y 1 x 2 k2 k1 2k 2 2k1
A particle is projected with a speed V from a point O making an angle of 30° with the vertical. At the same instant, a second particle is thrown vertically upwards from a point A. The two particle reach H, the highest point on the parabolic path of first particle simultaneously. The V is ratio v 2 (a) 3 2 (b) 2 3 (c) 3 The acceleration of a particle which moves along the positive x-axis varies with its position as shown. If the velocity of the particle is 0.8 m/s at x = 0 , the velocity (in m/s) of the particle at x = 1.4 is (a) 1.6 (b) 1.2 (c) 1.4 (d) none of these
H
V 30°
v O (d)
A 3 2
a (in m/s2)
0.4 0.2
O
0.4 0.8
1.4
x (in m)
5.
Two trains A and B leave the same station on parallel tracks. A starts with uniform 1 acceleration of m/s2 and attains a speed of 24 km/h. B leaves 40 s later with uniform 6 1 acceleration of m/s2 and attains a speed of 48 km/h. Find the time (in s) after which train 3 B will overtake train A.
6.
A gun kept on a straight horizontal road, is used to hit a car, tavelling along the same road away from the gun with the uniform speed of 90 km/h. The car is at a distance of 600 m
KINEMATICS
10
from the gun when shell is fired from the gun at an angle of 30° with the horizontal. Find the position (in m) from the initial position of the car at which the shell hits the car.
7.
A gun is situated on an inclined plane. The maximum range up the inclined plane and down the inclined plane are 250 m and 750 m respectively. Find the angle of inclination (in degree) of the inclined plane.
8.
In the figure shown, the two projectiles are fired simultaneously. Find the minimum distance (in m) between them during their flight? 203m/s 20m/s 60°
30°
20m
