Question

please solve the above questions 16 17 18.​

Answer 1

Answer:

16) a,b, d

17) a,b,c

18) b, d

Explanation:

16)

Known values :

Vo = velocity for both projection

$\theta _{1} \: = angle \: of \: projection \: for \: first \: and \\ \: \theta _{2} = \: angle \: of \: projection \: for \: second$

H1 > H2

also ,

$h \: = \frac{v_{0} {}^{2} \: \sin {}^{2} ( \theta) }{2g}$

since , v and 2g are constant for both we can say that,

h is Directly proportional to sin(∅)

means if H1 > H2 , then. sin(∅1) > sin(∅2)

and ∅ is acute angle so ,

∅1 > ∅2

option a >> is true ( correct )

Now, Time of flight =

$t \: = \frac{2v _{0} \sin( \theta) }{g}$

similarly , t directly varies with sin(∅) or ∅

So, T1 > T2 as ∅1 > ∅2

option b >> is true (correct)

Now, Range =

$r = \frac{ { v_{0} }^{2} \: \sin(2 \theta) }{g}$

R directly varies with sin(2∅)

But ,note we know ,∅1 > ∅2 and

let ∅1 = 30° and ∅2 = 60°

so, sin(2× ∅1 ) = sin(2 × ∅2) = √3/2

Thus , R1 is not always greater than R2.

so option c >> is false ( incorrect)

Total energy = U = mgH + ½ mv²

AS , WE KNOW , H1 > H2 and m , v, g are constant

so U1 > U2

option d >> is true ( correct)

Now comes the question number 17

If a particle is performing uniform circular motion then,

1) Its speed remains constant throughout the motion.

2)Tangential acceleration is always zero.

3)The magnitude of the radial acceleration is constant always.

a) option is correct

Magnitude of particle velocity must remain constant .

b) option is correct

Particle velocity remains directed perpendicular to radius vector.

c) option is correct

direction of acceleration keeps changing as particle moves

d) option is incorrect

Now comes question number 18

we know ,

|A + B| = √{A² + B² + 2|A||B|cos∅}

|A - B| = √{A² + B² - 2|A||B|cos∅}

Now we can see that

| A + B | = | A - B| is possible if 2|A||B|cos∅ is 0

i.e. 2|A||B|cos∅ = 0

=> |A||B|cos∅ = 0

so, we can conclude that ,

Either,

=> cos∅ = 0

=> ∅ = π/2 which means |A| perpendicular |B|

Or,

=> |A| = 0 else |B| = 0

So, we can say that

option b and d are correct.

option a and c are incorrect.