A pilot of mass $75 kg$ in a jet aircraft executes a loop with a constant speed of $360 km/hr$ . If the radius of the loop is $200 m$ , the force exerted by seat on the pilot at the top of the loop is $(Take g = 10 {m/s}^{2})$

3750 N

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4485 N

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3000 N

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5843 N

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Solution

The correct option is C $3000 N$
At the top most point, FBD of pilot:-

Here $N_{p s}$ is the normal on pilot by the seat in the downward direction
$v = 360 k m / h$ $= 360 \times \frac{5}{18}$
$\Rightarrow v = 100 m / s$
Applying Equation of dynamics :-
Net force on the pilot by the seat $N = \frac{m v^{2}}{R} - m g$

$= \frac{75 \times (100)^{2}}{200} - 75 \times 10$

$\Rightarrow$ Required net force $= (3750 - 750) N$
$= 3000 N$

Hence option C is the correct answer

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A pilot of mass 75 kg in a jet aircraft executes a loop with a constant speed of 360 km/hr. If the radius of the loop is 200 m, the force exerted by seat on the pilot at the top of the loop is (Take g=10 m/s2)

A pilot of mass $75 kg$ in a jet aircraft executes a loop with a constant speed of $360 km/hr$ . If the radius of the loop is $200 m$ , the force exerted by seat on the pilot at the top of the loop is $(Take g = 10 {m/s}^{2})$