A particle moves in the x -y plane under the action of a force F such that the value of its linear momentum P- at any time - t- is Px-2 cost- Py- 2 sint-The angle - between F- and P- at a given time t- will be

The correct option is C P_x = 2 cos t,P_y = 2 sin t ∴ P = 2cos t î + 2 sin t ĵ F = dP/dt = 2sin t î + 2 cos t ĵ F. P = 0 ...

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Byju's Answer

Standard XII

Physics

Second Law of Motion

A particle mo...

Question

A particle moves in the x-y plane under the action of a force F such that the value of its linear momentum $(\to P)$ at any time 't' is $P_{x} = 2 c o s t, P_{y} = 2 s i n t$ .The angle $θ$ between $\to F$ and $\to P$ at a given time t. will be

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Solution

The correct option is C

$P_{x} = 2 c o s t, P_{y} = 2 s i n t ∴ P = 2 c o s t^i + 2 s i n t^j$

$\to F = \frac{d \to P}{d t} = - 2 s i n t^i + 2 c o s t^j$

$\to F . \to P = 0$ $∴ θ = 90^{\circ}$

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A particle moves in the x-y plane under the action of a force F such that the value of its linear momentum (→P) at any time 't' is Px=2cost,Py=2sint.The angle θ between →F and →P at a given time t. will be

The correct option is C Px=2cost,Py=2sint∴P=2cost^i+2sint^j →F=d→Pdt=−2sint^i+2cost^j →F.→P=0 ∴θ=90∘

A particle moves in the x-y plane under the action of a force F such that the value of its linear momentum $(\to P)$ at any time 't' is $P_{x} = 2 c o s t, P_{y} = 2 s i n t$ .The angle $θ$ between $\to F$ and $\to P$ at a given time t. will be

The correct option is C

$P_{x} = 2 c o s t, P_{y} = 2 s i n t ∴ P = 2 c o s t^i + 2 s i n t^j$

$\to F = \frac{d \to P}{d t} = - 2 s i n t^i + 2 c o s t^j$

$\to F . \to P = 0$ $∴ θ = 90^{\circ}$