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Question Bank No: 2

1. The trajectory of a projectile as seen from another projectile is a

a)		circle
b)		parabola
c)		straight line
d)		ellipse

2. A large number of bullets are fired in all direction with the same speed v. What is the maximum area on the ground on which these bullets are spread?

a)		$\frac{π v^{4}}{g^{2}}$
b)		$\frac{π v^{2}}{g}$
c)		$\frac{π^{2} v^{2}}{g^{2}}$
d)		$\frac{π^{2} v^{2}}{g}$

3. A projectile can have the same range R for two angles of projection. If $t_{1}$ and $t_{2}$ be the times of flight in the twocases then what is the product of the two times of flight ?

a)		$t_{1} t_{2} α R$
b)		$t_{1} t_{2} α \frac{1}{R}$
c)		$t_{1} t_{2} α \frac{1}{R^{2}}$
d)		$t_{1} t_{2} α R^{2}$

4. A ball is dropped from the top of a tower in a high speed wind. The wind exerts a steady force on the ball. The path followed by the ball will be

a)		circular arc
b)		straight line
c)		elliptical arc
d)		parabola

5. The range of projectile when launched at angle $θ$ is same as when launched at angle 2 $θ$ . What is the value of $θ ?$

a)		$30^{0}$
b)		$60^{0}$
c)		$15^{0}$
d)		$45^{0}$

6. Which of the following is the largest, when the height attained by the projectile is the greatest ?

a)		Time of height
b)		Angle of projectile with the verticle
c)		Range
d)		Horizontal component of velocity

7. A vector $\vec{a}$ is rotated through an angle $θ$ , what is the magnitude of change in vector?

a)		$2 a \cos \frac{θ}{2}$
b)		$2 a \sin \frac{θ}{2}$
c)		$2 a \cos θ$
d)		$2 a \sin θ$

8. The momentum of a particle is $\vec{p} = 2 \cos θ \hat{i}$ +2 sin $θ \hat{j}$ . What is the angle between the force $\vec{F}$ acting on the particle and the momentum $\vec{p}$

a)		$65^{0}$
b)		$90^{0}$
c)		$150^{0}$
d)		$180^{0}$

9. For what value of a, $\vec{A} = 2 \hat{i} + a \hat{j} + \hat{k}$ will be perpendicular to $\vec{B} = 4 \hat{i} - 2 \hat{j} + \hat{k}$ ?

a)		4
b)		0
c)		3
d)		1

10. The point of application of a force 5 $\hat{i} + 4 \hat{j}$ +10 $\hat{k}$ metere to 7 $\hat{i} + 7 \hat{j}$ +8 $\hat{k}$ metre. What is the gain in kinetic energy of the system?

a)		81 J
b)		49 J
c)		11 J
d)		9 J

11. The resultant of two forces $(A + B)$ and $(A - B)$ is a force $\sqrt{3 A^{2} + B^{2}}$ . The angle between two given forces is

a)		$\frac{π}{4}$
b)		$\frac{π}{3}$
c)		$\frac{π}{2}$
d)		$π$

12. The vector sum of two vectors $\hat{P}$ and $\hat{Q}$ is $\hat{R}$ . If $\hat{Q}$ is reversed, the resultnat becomes $\hat{S}$ then which of the following relation is valid :

a)		$R^{2} + S^{2} = P^{2} + Q^{2}$
b)		$R^{2} + S^{2} = 2 (P^{2} + Q^{2})$
c)		$R^{2} - S^{2} = 2 (P^{2} - Q^{2})$
d)		R +S = 2 $(P + Q)$

13. What is the component of 3 $\hat{i} + 4 \hat{j}$ along $\hat{i} + \hat{j}$ ?

a)		$\frac{3}{2}$ $(\hat{i} + \hat{j})$
b)		$\frac{7}{2}$ $(\hat{i} + \hat{j})$
c)		$\frac{1}{2} (\hat{i} + \hat{j})$
d)		$\frac{5}{2}$ $(\hat{i} + \hat{j})$

14. Given that $| \vec{P} + \vec{Q} | = | \vec{P} - \vec{Q} |$ , In which of the following cases, this relation is not true?

a)		$\vec{P} ⊥ \vec{Q}$
b)		$\vec{P} ∥ \vec{Q}$
c)		$\vec{P}$ is a null vector
d)		$\vec{Q}$ is a null vector

15. Three forces a $(\hat{i} - \hat{j} + \hat{k})$ , $(2 \hat{i} - 3 \hat{j} + 4 \hat{k})$ and $(8 \hat{i} - 7 \hat{j} + 6 \hat{k})$ keep the body in equilibrium, then the value of a is

a)		20
b)		-20
c)		10
d)		-10

16. A person moves 30 m north, then 20m east and finally 30 $\sqrt{2}$ m south west. The displacement of the person from the original position is

a)		10 m west
b)		10 m east
c)		75 m north-east
d)		75 m north-west

17. If the two vectors 4 $\hat{i} + 8 \hat{j} + 6 \hat{k}$ and 2 $\hat{i} + 4 \hat{j} + b \hat{k}$ are parallel to each other, then what is the value of b?

a)		3
b)		$\frac{- 20}{3}$
c)		$- 3$
d)		6

18. If the angle $α$ between two forces of equal magnitude is reduced to $(α - \frac{π}{3})$ , then the magnitude of the resultant becomes $\sqrt{3}$ times of the earlier one. The angle $α$ is

a)		$\frac{π}{4}$
b)		$\frac{2 π}{3}$
c)		$\frac{4 π}{5}$
d)		$\frac{π}{2}$

19. A car is moving in a circular horizontal track of radius 10m with a constant speed of 10 m/s. A plumb hole is suspended from the roof of the car by a light rigid rod of length 1m. The angle made by the rod with the track is

a)		Zero
b)		$30^{0}$
c)		$45^{0}$
d)		$60^{0}$

20. A small body of mass m is placed on the top of an hemisphere of radius r. Then the smallest horizontal velocity v that should be given to the body so that it may leave the hemispherical surface and not slide down.

a)		$\sqrt{gr}$
b)		$\sqrt{2 gr}$
c)		$\sqrt{3 gr}$
d)		$\sqrt{5 gr}$

21. A tank is filled with water upto a height H. Water is allowed to come out of a hole P in one of the walls at a depth h, below the surface. The horizontal distance is maximum when

a)		h =H
b)		h=0
c)		h = $\frac{H}{2}$
d)		$h = \frac{H}{3}$

22. Where will it be profitable to purchase 1 kg sugar by an ordinary balance?

a)		At poles
b)		At equator
c)		At $45^{0}$ latitude
d)		Same at all above places

23. The mass M rests on the top of a hemisphere of a radius R. What minimum horizontal velocity should be imparted to the mass, so that it leaves the hemisphere without sliding over it.

a)		$\sqrt{gR}$
b)		$\sqrt{2 gR}$
c)		$\sqrt{3 gR}$
d)		$\sqrt{4 gR}$

24. A body is projected up a $45^{0}$ rough incline. The coefficient of friction is 0.5. Then the retardation of the block is

a)		$g / 2 \sqrt{2}$
b)		$g / \sqrt{2}$
c)		$3 g / 2 \sqrt{2}$
d)		$g / 2$