Question

guys please answer this question......no spam please...​

Answer 1

Answer: option d is incorrect.

Explanation has been given in image. i hope you understand.

Answer 2

Question :

The position vector of a particle R as a function of time is given by :-

• R = 4 sin(2πt) i + 4 cos(2πt) j

where R is in meters, t is in second and i and j denote unit vectors along x and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?

Answer :

The position vector of a particle R as a function of time is given by :-

• R = 4 sin(2πt) i + 4 cos(2πt) j

x-component : x = 4 sin 2πt ..... (i)

y-component : y = 4 cos 2πt ..... (ii)

Squaring and adding both equations, we get

x² + y² = 4² [sin²(2πt)+cos²(2πt)]

x² + y² = 4²

Eq. of circle : x² + y² = R²

• R denotes radius of circle

∴ Radius of circle = 4 m

[Option - A is correct]

_________________________

Acceleration vector is given by

• a = v²/R $\bf{\hat{-R}}$

∴ Acceleration vector is along -R.

[Option - B is correct]

_________________________

Magnitude of acceleration vector,

• a = v²/R

where v is the velocity of particle.

[Option - C is correct]

_________________________

x-component of velocity

• v(x) = 4 (cos 2πt) 2π

y-component of velocity

• v(y) = -4 (sin 2πt) 2π

Resultant velocity of particle,

➝ v = √[v²(x) + v²(y)]

On solving we get,

➝ v = 8π m/s

[Option - D is incorrect]