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First Law of Motion

10. A force v...

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10. A force vector f=vector v × vector A is exerted on a particles in addition to the force of gravity, where vector v is the velocity of the particlesand vector A is a constant vector in the horizontal direction. With what minimum speed a particle of mass m be projected so that it continues to move undeflected with a constant

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F = v \times A

is exerted on a particle in addition to the force of gravity, where

v

is the velocity of the particle and

A

is a constant vector in the horizontal direction. With what minimum speed a particle is mass

m

be projected so that it continues to moved undeflected with a constant velocity?

Q. In a certain region free from gravity, electric field is along negative x-direction and it is constant. A particle having mass m and charge q is projected along x-direction with speed

V_{0}

. An additional force

\to F = \to C \times \to V

is acting on the charge where

\to V

is velocity vector and

\to C

is a constant vector. The charge comes out of region with speed

\frac{V_{0}}{2}

as shown in figure, then the magnitude of electric field is :

Q. A particle of mass 'm' is projected with velocity 'u' at an angle

θ

with horizontal. During the period when the particle descends from highest point to the position where its velocity vector makes an angle

\frac{θ}{2}

with horizontal, work done by the gravity force is

Q. A charged particle with charge q enters a region of constant ,uniform abd mutually orthogonal fields E vector and B vector with a velocity Vvector perpendicular to both E vector and B vector, and comes out without any change in magmituse or direction of V vector, then V vector will be in terms of B and E

A

moves in one direction along a given trajectory with a tangential acceleration

ω_{τ} = a τ

\to a

is a constant vector coinciding in direction with the

x

axis as shown in figure above, and

\to τ

is a unit vector coinciding in direction with the velocity vector at a given point. Find how the velocity of the particle depends on

x

provided that its velocity is negligible at the point

x = 0

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