CAREER POINT, CP Tower, IPIA, Road No.1, Kota (Raj.), Ph: 0744-5151200 www.careerpoint.ac.in Page # 1

CAREER POINT

Fresher Course for IIT JEE (Main & Advanced)–2017

DAILY PRACTICE PROBLEM SHEET Course : Fresher(XL) Batch Subject : Physics DPPS 1

Topic : Kinematics Q.1 a projectile is fired with velocity v at angle of θ with horizontal. What would be the radius of curvature of

path at instant when rate of change of speed of projectile is minimum?

(A) g

v θ22 cos (B) θcos

2

gv (C)

gv θcos2

(D) θ2

2

cosgv

Q.2 A particle is hurled into air from a point on the horizontal ground at an angle with the vertical. If the air exerts a resistive force proportional to the speed of the projectile

(A) the path of the projectile will be symmetrical about the vertical line through its highest position (B) At the highest point, the velocity is horizontal (C) The time for ascent equal the time for descent (D) the total energy of the projectile is conserved Q.3 The retardation of a particle varies with instantaneous velocity 'v' as a = – αv where α is a small constant. If

the velocity of the particle is v0 at t = 0. Then -

(A) The total distance covered by the particle will be α

0v

(B) The particle will continue to move for a very long time (t → ∞)

(C) Velocity will decrease by 50% in a time of α1

(D) All the above Q.4 A particle is projected from the horizontal surface in earth's gravitational field at an angle θ with the

horizontal then -

(A) Center of curvature of projectile's trajectory at the highest point is below the horizontal surface level if θ < tan–1 2

(B) Center of curvature of projectile's trajectory at the highest point is below the horizontal surface if θ < tan–1 2

(C) Center of curvature of projectile's trajectory at the highest point is below the ground level is θ > tan–1 2

(D) irrespective of the value of θ centre of curvature always lies below the horizontal surface of the earth

Q.5 Two runners in a 120 metre start from the same place, but one runner gives the other a little advantage. The first runner, Albert, starts right away and runs at a constant velocity of 8.0 m/s. The second runner, Henry, waits for two seconds and then runs at a velocity of 9.0 m/s. How far (in m) is the winner ahead of the other runner at the end of the race ?

CAREER POINT, CP Tower, IPIA, Road No.1, Kota (Raj.), Ph: 0744-5151200 www.careerpoint.ac.in Page # 2

Q.6 A particle P is initially at a distance d = 16 m form point O. The particle P moves with a velocity

v = 5^

PO + i3 . Where ^

PO is a unit vector from P to O at any time t. Initially ^

PO is perpendicular to i . Find

the time in seconds after which point P meets points O.

(A) 5 (B) 4 (C) 8 (D) None of these Q.7 A bird is at a point P (4 m, –1 m, 5 m) and sees two point P1(–1 m, –1 m, 0 m) and P2 (3 m, –1 m, –3 m). At time

t = 0, it starts flying in a plane of the three positions, with a constant speed of 2 m/s in a direction perpendicular to the straight line P1 P2 till it sees P1 & P2 collinear at time t. Find the time t.

(A) 3.5 sec. (B) 4 sec. (C) 4.5 sec. (D) 5 sec. Q.8 A particle is moving along straight line with velocity v = t2 – 3t + 2 m/s. Particle will retard for time t if - (A) t < 1 (B) 1 < t < 1.5 (C) 1.5 < t < 2 (D) t > 2

Q. 9 Hailstones falling vertically with a speed of 10 m/s, hit the wind screen (wind screen makes an angle 30° with horizontal) of a moving car and rebound elastically. Find the velocity of the car driver finds the hailstones rebound vertically after striking.

(A) 10 3 m/s (B) 10/ 3 m/s (C) 3/5 m/s (D) 5/3 m/s Q.10 In the arrangement shown, the rod is pivoted at point O and is in contact with the block which moves on the

horizontal frictionless ground as shown. As the block is given a speed v in forward direction, the rod rotates about point O. Find the angular velocity of the rod as a function of θ.

θ Oh

v

(A) θ2sinhv (B) θsin

hv (C) θcos

hv (D)

θsinhv

Q.11 A ball is dropped from a height of 49 m and wind blows horizontally & imparts the constant acceleration of

4.90 m/sec2 to the ball. Choose the correct statement's [g = 9.8 m/sec2] (A) Path of the ball is straight line (B) Path of the ball is curved line (C) Time taken by the ball to reach the ground is 3.16 sec (D) The acute angle made by the line joining initial & final position (on ground) of the ball with horizontal is

more than 45º Q.12 A particle is thrown from a stationary platform with velocity v at an angle of 60° with the horizontal. The

range obtained is R. If the platform was moving horizontally in the direction of target with velocity v, and particle was thrown with same speed v (w.r.t. platform) at same angle, then the range would have been -

(A) 3R/2 (B) 5R/2 (C) 2R (D) 3R

CAREER POINT, CP Tower, IPIA, Road No.1, Kota (Raj.), Ph: 0744-5151200 www.careerpoint.ac.in Page # 3

Q.13 A car starts moving rectilinearly, first with acceleration a = 5.0 m/s2 (the initial velocity is equal to zero), then uniformly and finally, decelerating at the same rate a, comes to a stop. The total time of motion equals t = 25 s. The average velocity during that time is equal to <v> = 72 km per hour. The car move uniformly for the time 5n sec. Find 'n'

Q.14 A particle is projected with initial velocity v = 10 2 m/s as shown. After elastic collision with the inclined plane the particle rebounds normally with the plane and retraces its path to come back at its point of projection. Then find the time in seconds in which particle returns to the point of projection. (g = 10 m/s2)

α = sin –1

31v

Q.15 A particle is projected from ground with minimum speed required to hit a target at a height h = 10 m at

a horizontal distance d = 300 m as shown. Then find the time taken by particle (in seconds) to hit the target. (g = 10 m/s2)

d

Target

h

ANSWERS

1. (A) 2. (C) 3. (A,B) 4. (A) 5. 3 6. (A) 7. (A)

8. (A,C) 9. (A) 10. (A) 11. (A,C,D) 12. (D) 13. 3 14. 6

15. 2