Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise (Assertion & Reason)>Q 16

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Six vectors, $\vec{a}$ through $\vec{f}$ have the magnitudes and directions indicated in the figure. Which of the following statements is true?

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Important Questions on Mathematical Tools in Physics

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Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise (Assertion & Reason)>Q 17

If vectors

\vec{A} = \cos (ω t) \hat{i} + \sin (ω t) \hat{j}

and

\vec{B} = \cos (\frac{ω t}{2}) \hat{i} + \sin (\frac{ω t}{2}) \hat{j}

are functions of time then the value of

t

at which they are orthogonal to each other is,

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Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise (Assertion & Reason)>Q 18

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is,

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Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise (Assertion & Reason)>Q 19

If

3 cosθ + 4 sinθ = Asin (θ + α)

, then values of

A

and

α

are

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Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise (Assertion & Reason)>Q 20

If velocity of a particle is given by

v = (2 t + 3) m s^{- 1}

, then average velocity in the interval

0 \leq t \leq 1 s

is:

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Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise (Assertion & Reason)>Q 21

The kinetic energy of a particle of mass

m

moving with speed

v

is given by

K = \frac{1}{2} m v^{2}

. If the kinetic energy of a particle moving along

x

-axis varies with

x

as

K (x) = 9 - x^{2}

. Then the region in which the particle lies is:

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Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise (Assertion & Reason)>Q 22

The sum of magnitudes of two forces acting at a point is

16 N

. If the resultant force is

8 N

and its direction is perpendicular to a smaller force, then the forces are:

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Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise (Assertion & Reason)>Q 23

At what angle must the two forces

(x + y)

and

(x - y)

act so that the resultant maybe

\sqrt{(x^{2} + y^{2})}

?

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Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise (Assertion & Reason)>Q 24

A vector of length

l

is turned through the angle

θ

about its tail. What is the change in the position vector of its head?