A particle moves in the plane under the influence of a force such that its linear momentum is , where and are constants. The angle between the force and the momentum is [2007]

Question

A particle moves in the $X - Y$ plane under the influence of a force such that its linear momentum is $\vec{p} (t) = A [\hat{i} \cos (k t) - \hat{j} \sin (k t)]$ , where $A$ and $k$ are constants. The angle between the force and the momentum is [2007]

Smart Achievers · Accepted Answer

(4)

$Given: momentum \vec{p} (t) = A [\hat{i} \cos (k t) - \hat{j} \sin (k t)]$

$And, force \vec{F} = \frac{d \vec{p}}{d t} = A k [- \hat{i} \sin (k t) - \hat{j} \cos (k t)]$

$Here, \vec{F} \cdot \vec{p} = 0 But \vec{F} \cdot \vec{p} = F p \cos θ$

$∴$ $\cos θ = 0 \Rightarrow θ = 90 °$

$Hence, angle between the force and momentum, θ= 90 ° .$

Solution

Q.
A particle moves in the $X - Y$ plane under the influence of a force such that its linear momentum is $\vec{p} (t) = A [\hat{i} \cos (k t) - \hat{j} \sin (k t)]$ , where $A$ and $k$ are constants. The angle between the force and the momentum is [2007]

1 $0 °$

2 $30 °$

3 $45 °$

4 $90 °$

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Solution

Q. A particle moves in the X-Y plane under the influence of a force such that its linear momentum is p→(t)=A[i^cos(kt)-j^sin(kt)], where A and k are constants. The angle between the force and the momentum is [2007]

1 0°

2 30°

3 45°

4 90°