J J Science Academy - Physics Test

1. The coordinates of a moving particle at time t are given by $x=ct^{3}$ and $y=bt^{3}$. The speed of the particle, $at t=1$ s, is

1) $3 \sqrt{c^{2}+b^{2}}$2) $3 (c+b)$3) $\frac{1}{3} \sqrt{c^{2}+b^{2}}$4) $3 \sqrt{c^{2}-b^{2}}$

2. Five balls $A, B, C, D$ and E are projected with the same speed making angles $10^{\circ}, 30^{\circ}, 45^{\circ}, 60^{\circ}$ and $80^{\circ}$ respectively with the horizontal. Which ball will strike the ground at the farthest point?

1) A2) E3) D4) C

3. On which of the following, is the maximum height achieved by a projectile, independent?

1) vertical component of the initial velocity2) Angle of projection3) Acceleration due to gravity4) horizontal component of initial velocity

4. The angle of projection for same maximum range is

1) $45^{\circ}$2) $53.5^{\circ}$3) $63^{\circ}$4) $73^{\circ}$

5. If $R$ is the range of a projectile motion, then equation of its trajectory is

1) $y=x \cot \theta\left(1-\frac{x}{R}\right)$2) $y=x \cot \theta\left(1+\frac{x}{R}\right)$3) $y=x \tan \theta\left(1-\frac{x}{R}\right)$4) $y=x \tan \theta\left(1+\frac{x}{R}\right)$

6. In a projectile motion, the velocity

1) is always perpendicular to the acceleration.2) is never perpendicular to the acceleration.3) is perpendicular to the acceleration for one instant only.4) is perpendicular to the acceleration for two instants.

7. Two projectiles are fired with same speed with two different angles of projections, so as to have same range $R$. If the maximum height reached by them are $h_{1}$ and $h_{2}$, then $R=$

1) $\frac{4 h_{1} h_{2}}{h_{1}+h_{2}}$2) $\frac{4 h_{1} h_{2}}{h_{1}-h_{2}}$3) $4 \sqrt{h_{1} h_{2}}$4) $2 \sqrt{h_{1} h_{2}}$

8. A particle is projected with a velocity v so that its horizontal range is twice the greatest height attained. The horizontal range is

1) $\frac{4 v^{2}}{5 g}$2) $\frac{v^{2}}{g}$3) $\frac{v^{2}}{2 g}$4) $\frac{2 v^{2}}{3 g}$

9. A ball is projected with a speed of $40 m / s$ at an angle $45^{\circ}$ with horizontal. There is a wall of 50 m height at a distance of 40 m from the projection point. The ball will hit the wall at a height of

1) 10 m2) 20 m3) 30 m4) 40 m

10. A particle moves in the X-Y plane according to the law $x=kt$ and $y=kt(1-\alpha t)$, where k and $\alpha$ are positive constants and $t$ is time. What is the equation of trajectory of the particle?

1) $y=k x$2) $y=x-\frac{\alpha x^{2}}{k}$3) $y=-\frac{\alpha x^{2}}{k}$4) $y=\alpha x$

11. For a projectile motion, if $x=8 t$ and $y=2 t-3 t^{2}$, then its time of flight is

1) $\frac{2}{3} s$2) $\frac{1}{3} s$3) $\frac{4}{3} s$4) $\frac{5}{3} s$

12. A shell fired from a canon can cover maximum horizontal distance of 10 km . Then velocity of projection is

1) $\sqrt{980} m / s$2) $\sqrt{9800} m / s$3) $\sqrt{98000} m / s$4) $10^{2} \sqrt{98} m / s$

13. A particle of mass m is projected with velocity v making an angle of $45^{\circ}$ with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be

1) $\frac{mv}{\sqrt{2}}$2) $\sqrt{2} mv$3) 04) 2 mv

14. Two boys stationed at A and B fire bullets simultaneousllly at a bird stationed at C . The bullets are fired from A and B at an angles of $53^{\circ}$ and $37^{\circ}$ respectively with the vertical. Both the bullets hit the bird simultaneously. If $v_{B}=60 m / s$, then $v_{A}=(\tan 37=\frac{3}{4})$

1) $80 m / s$2) $40 m / s$3) $45 m / s$4) $90 m / s$

15. A stone is projected with a velocity $20 \sqrt{2} m / s$ at an angle of $45^{\circ}$ to the horizontal. The average velocity of stone during its motion from starting point to its maximum height is (take $g=10 m / s^{2})$

1) $20 m / s$2) $20 \sqrt{5} m / s$3) $5 \sqrt{5} m / s$4) $10 \sqrt{5} m / s$

16. If 2 balls are projected at angles $45^{\circ}$ and $60^{\circ}$ and the maximum heights reached are same, what is the ratio of their initial velocities?

1) $\sqrt{2}: \sqrt{3}$2) $\sqrt{3}: \sqrt{2}$3) 3: 24) 2: 3

17. The angle of projection, for which the horizontal range and the maximum height of a projectile are in the ratio of $2: 1$ is

1) $45^{\circ}$2) $\theta=\tan ^{-1}(0.25)$3) $\theta=\tan ^{-1}(2)$4) $60^{\circ}$

18. The equation of a path of a projectile is $y=\frac{x}{\sqrt{3}}-\frac{1}{2} gx^{2}$. The angle of projection with the vertical is

1) $30^{\circ}$2) $60^{\circ}$3) $45^{\circ}$4) $53^{\circ}$

19. A body is projected with initial velocity of $(8 \hat{i}+6 \hat{j}) m / s$. The horizontal range is

1) 9.6 m2) 14 m3) 50 m4) 24.6 m

20. The range of a particle when launched at an angle of $15^{\circ}$ with the horizontal is 150 m . What is the range of projectile, when launched at an angle of $45^{\circ}$ to the horizontal?

1) 150 m2) 300 m3) 450 m4) 600 m

21. Two stones having different masses $m_{1}$ and $m_{2}$ are projected at angles $\theta$ and $(90^{\circ}-\theta)$ with same velocity from the same point. The ratio of their maximum heights is

1) 1: 12) 1: $\tan \theta$3) $\tan \theta: 1$4) $\tan ^{2} \theta: 1$

22. The equation of path of a projectile is $y=x-20 x^{2}$. The maximum height reached by the body, above the point of projection is

1) $\frac{1}{80}$2) $\frac{1}{1600}$3) $\frac{1}{40}$4) $\frac{1}{320}$

23. A stone is projected from the ground with velocity $50 m / s$ at an angle of $30^{\circ}$. It crosses a wall after 3 s . How far beyond the wall the stone will strike the ground? [ $g=10 m / s^{2})$

1) 90.2 m2) 89.6 m3) 86.6 m4) 70.2 m

24. Two projectiles, one fired from the surface of the earth with speed $5 m / s$ and other fired from the surface of a planet with initial speed of $3 m / s$, traces identical trajectories. Neglecting friction effect, the value of acceleration due to gravity on the planet is

1) $5.9 m / s^{2}$2) $3.5 m / s^{2}$3) $16.3 m / s^{2}$4) $8.5 m / s^{2}$

25. From the top of a tower, three balls $A, B$ and C whose mass is in the ratio $1: 2: 3$ are thrown with the same speed $v_{0}$ as shown. The ratio of speed with which they strike the ground is

1) 1: 2: 32) 1: 1: 13) 3: 2: 14) 1: 4: 9

26. A body, of mass 4 kg , is fired with velocity $(5 \hat{i}+4 \hat{j}) ms^{-1}$. Its minimum kinetic energy will be

1) $50 \sqrt{2} J$2) 100 J3) 50 J4) $25 \sqrt{2} J$

27. The equation of a projectile path is given by, $y=\sqrt{3} x-x^{2}$. The range of motion is

1) 3 m2) $3 \sqrt{3} m$3) $\sqrt{3} m$4) $1 / \sqrt{3} m$

28. The equation of a projectile path is given by, $y=\sqrt{3} x-x^{2}$. Maximum height reached by the body is

1) $\sqrt{3} m$2) 0.75 m3) 0.5 m4) $\frac{\sqrt{3}}{2} m$

29. The equation of a projectile path is given by, $y=\sqrt{3} x-x^{2}$. The angle of projection is

1) 752) $30^{\circ}$3) $60^{\circ}$4) $45^{\circ}$

30. The equation of a projectile path is given by, $y=\sqrt{3} x-x^{2}$. The velocity at the highest point is

1) $\sqrt{5} m / s$2) $\sqrt{3} m / s$3) $\sqrt{10} m / s$4) $\frac{\sqrt{5}}{2} m / s$

31. The equation of a projectile path is given by, $y=\sqrt{3} x-x^{2}$. The velocity of projection is

1) $\frac{\sqrt{5}}{2} m / s$2) $\sqrt{3} m / s$3) $\sqrt{10} m / s$4) $2 \sqrt{5} m / s$

32. Three projectiles are fired at an angle of projection of $20^{\circ}, 45^{\circ}, 70^{\circ}$, with same velocity. Their range is X , Y and Z . Then

1) $X=Y2) $X=Z>Y$3) $X=Y>Z$4) $X=Z

33. Three projectiles are fired at an angle of projection of $20^{\circ}, 45^{\circ}, 70^{\circ}$, with same velocity. If the maximum heights reached by the projectiles are $H_{1}, H_{2}$ and $H_{3}$, then $H_{1}+H_{3}=$

1) $H_{2} / 2$2) $2 H_{2}$3) $4 H_{2}$4) $H_{2}$

34. Three projectiles are fired at an angle of projection of $20^{\circ}, 45^{\circ}, 70^{\circ}$, with same velocity. If the time of flights of the projectiles are $T_{1}, T_{2}$ and $T_{3}$, then $T_{1}^{2}+T_{3}^{2}=$

1) $T_{2}^{2} / 2$2) $2 T_{2}^{2}$3) $4 T_{2}^{2}$4) $T_{2}^{2}$

35. A body is projected with a velocity of $10 m / s$ at angle of projection of $60^{\circ}$. Its velocity at the end of $1 / \sqrt{3} s$ is $(g=10 m / s^{2})$

1) $5 \hat{i}+5 \sqrt{3} \hat{j} m / s$2) $5 \hat{i}+\frac{5 \sqrt{3}}{3} \hat{j} m / s$3) $5 \hat{i}+\frac{5 \sqrt{3}}{2} \hat{j} m / s$4) $5 \hat{i}+\frac{5 \sqrt{3}}{4} \hat{j} m / s$

36. A body is projected with a velocity of $10 m / s$ at angle of projection of $60^{\circ}$. The velocity of the body when it attains a height of $\frac{15}{4} m$ is

1) $5 \hat{i}-5 \sqrt{3} \hat{j} m / s$2) $5 \hat{i} m / s$3) $5 \hat{i}+\frac{5 \sqrt{3}}{2} \hat{j} m / s$4) $5 \hat{i}+\frac{5 \sqrt{3}}{4} \hat{j} m / s$

37. A body is projected horizontally with a velocity $3 m / s$ and another with a speed of $30 m / s$. The time taken by the first to reach the ground is ______ that taken by the second.

1) less2) more3) $(1 / 10)^{th})$4) same

38. A body is projected from the ground with a velocity $\vec{v}=(3 \hat{i}+10 \hat{j}) m / s$. The maximum height attained and the range of the body respectively are (given $g=10 ms^{-2})$

1) 5 m and 6 m2) 3 m and 10 m3) 6 m and 5 m4) 3 m and 5 m

39. Two projectiles A and B are thrown with the same speed but angles of $40^{\circ}$ and $50^{\circ}$ with the horizontal. Which projectile will fall earlier?

1) A2) B3) Both will fall at the same time4) None of the above

40. If $R$ is the range of a projectile motion, then equation of its trajectory is

1) $y=x \cot \theta\left(1-\frac{x}{R}\right)$2) $y=x \cot \theta\left(1+\frac{x}{R}\right)$3) $y=x \tan \theta\left(1-\frac{x}{R}\right)$4) $y=x \tan \theta\left(1+\frac{x}{R}\right)$

41. For a given velocity, a projectile has the same range R for two angles of projection. If $t_{1}$ and $t_{2}$ are the times of flight in the two cases, then

1) $t_{1} t_{2} \propto R^{2}$2) $t_{1} t_{2} \propto R$3) $t_{1} t_{2} \propto \frac{1}{R}$4) $t_{1} t_{2} \propto \frac{1}{R^{2}}$

42. If a particle is thrown at an angle with horizontal and time of flight T and range of projectile R are 10 second and 200 m , the velocity of projection is

1) $10 \sqrt{29} m / s$2) $5 \sqrt{29} m / s$3) $15 \sqrt{29} m / s$4) $20 \sqrt{29} m / s$

43. A ball rolls off the edge of a horizontal plane 4.9 m high. If it strikes the floor at a point 10 m horizontally away from the edge of the plane, speed of the ball at the instant it left the plane is

1) $10 ms^{-1}$2) $20 ms^{-1}$3) $30 ms^{-1}$4) $40 ms^{-1}$

44. A particle is projected at an angle of $60^{\circ}$ above the horizontal with a speed of $10 m / s$. After some time the direction of its velocity makes an angle of $30^{\circ}$ above the horizontal. The speed of the particle at this instant is

1) $\frac{5}{\sqrt{3}} m / s$2) $5 \sqrt{3} m / s$3) $5 m / s$4) $\frac{10}{\sqrt{3}} m / s$

45. The range of projectile projected at an angle $15^{\circ}$ is $10 \sqrt{3} m$. If it is fired with the same speed at angle of $30^{\circ}$, then its range will be

1) 60 m2) 45 m3) 30 m4) 15 m