Question

A particle moves in the x - y plane under the influence of a force such that its linear momentum is p(t) = [i cos(at) - sin(at)] B, where a and B are constants. The angle between the force and the momentum is (1) 0 (2) 45° (3) 60° (4) 90° ​

Answer 1

Answer:

4)th option bro

Explanation:

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Class 11

>>Physics

>>Systems of Particles and Rotational Motion

>>Linear Momentum of a System of Particles

>>A particle moves in the x - y plane unde

Question

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A particle moves in the x-y plane under the influence of a force such that its linear momentum is

p

(t)=A(icos(kt)−jsin(kt)] where A and k are constants. The angle between the force and

momentum is

Medium

Solution

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Correct option is D)

P(t)=A(

j

^

coskt−

j

^

sinkt)

F=

dt

dP(t)

F=

dt

d

A(−

i

^

coskt−jsinkt)

=A(−

i

^

sinkt(k)−jcoskt(k))

F=Ak(−

i

^

sinkt−jcoskt)

Angle between two vectors is θ

cosθ=

∣F∣∣P∣

F.P

=A

∣F∣∣P∣

(

j

^

coskt−

j

^

sinkt).Ak(−

i

^

sinkt−

j

^

sinkt)

∣F∣∣P∣

A

2

k(−sinktcoskt+sinktcoskt)

=A

2

k(0)=0

θ=cos

−1

(0)=90

0