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A particle is performing circular motion in a circle of radius $R$ with variable speed, $v = Kt (K > 0) .$ Time when angle between acceleration vector and its velocity vector becomes $\frac{π}{4},$ is $4 \sqrt{\frac{R}{nK}} .$ The value of $n$ is _____.

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Important Questions on Motion in a Plane

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Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 54

A particle moves along a curve

y = x^{2}

with constant speed of

10 m s^{- 1} .

When the particle is at origin, then the radius of curvature of path is

n m .

The value of

n

is _____.

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Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 1

A particle moves on the curve

y = \frac{x^{2}}{4},

where

x = \frac{t}{2} .

x

and

y

are measured in metre and

t

in second. At

t = 4 s,

the velocity of particle is

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Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 2

One second after projection, a stone moves at an angle of

45 °

with the horizontal. Two seconds after projection, it moves horizontally. Its angle of projection is (in degrees)

(g = 10 m s^{- 2})

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Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 3

The horizontal range of a projectile is

R

and the maximum height attained by it is

H .

A strong wind now begins to blow in the direction of horizontal motion of projectile, giving it a constant horizontal acceleration equal to

g .

Under the same conditions of projection, the new range will be
(

g =

acceleration due to gravity)

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Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 4

The speed of a projectile when it is at its maximum height is

\sqrt{\frac{2}{5}}

times its speed at half the maximum height. What is its angle of projection?

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Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 5

If the horizontal range of projectile be a and the maximum height attained by it is

b,

then velocity of projection is

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Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 6

A ship is traveling due east at

10 km h^{- 1}

. A ship heading

30 °

east of north is always due north from the first ship. The speed of the second ship in

km h^{- 1}

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Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 7

An object moves at constant speed along a circular path in a horizontal $x y$ plane, with center at origin. When the object is at $x = - 2 m,$ its velocity is $- 4 \hat{j} m s^{- 1} .$ Its acceleration when it is at $y = 2 m$ is

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A particle is performing circular motion in a circle of radius R with variable speed, v=Kt (K>0). Time when angle between acceleration vector and its velocity vector becomes π4, is 4RnK. The value of n is _____.

Important Questions on Motion in a Plane

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A particle is performing circular motion in a circle of radius $R$ with variable speed, $v = Kt (K > 0) .$ Time when angle between acceleration vector and its velocity vector becomes $\frac{π}{4},$ is $4 \sqrt{\frac{R}{nK}} .$ The value of $n$ is _____.