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Second Law of Motion

If P x =sin...

Question

If $P_{x} = sin t$
and $P_{y} = cos t$
where $P$ stands for momentum and x,y stands for the co-ordinate directions.
The angle between the applied force and the momentum at any time is

0 °

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30 °

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60 °

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90 °

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Solution

The correct option is B $90 °$
To determine the angle between the applied
force and momentum, let us resolve into horizontal and vertical components,
$P_{x} = s i n t$ and $P_{y} = c o s t$
$∴$ Resultant momentum, $P = \sqrt{P {_{x}}^{2} + {P_{y}}^{2}} = 1$
Since, the magnitude of resultant momentum is independent of time, the force must be at right angles to the instantaneous velocity or instantaneous momentum, as in case of circular motion.
So, the correct option is ( $d$ ).

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If Px=sintand Py=costwhere P stands for momentum and x,y stands for the co-ordinate directions.The angle between the applied force and the momentum at any time is

If $P_{x} = sin t$
and $P_{y} = cos t$
where $P$ stands for momentum and x,y stands for the co-ordinate directions.
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