JEE Main · 2021 · 16 Mar 2021 · Shift 1 · Vector

Consider a frame that is made up of two thin massless rods

A B

and

A C

as shown in the figure. A vertical force

P

of magnitude 100 N is applied at point A of the frame. Suppose the force is

P

resolved parallel to the arms AB and AC of the frame. The magnitude of the resolved component along the arm AC is xN.
The value of x , to the nearest integer, is
[Given :

sin (3 5^{\circ}) = 0.573, cos (3 5^{\circ}) = 0.819

sin (11 0^{\circ}) = 0.939, cos (11 0^{\circ}) = - 0.342]

Answer: 82

Solution

From the figure, angle BAC = 35°. The angle between the vertical force P and arm AC is 35°. Using Lami's theorem or resolving forces: the component along AC is given by

F_{A C} = \frac{P s i n ( ∠ A B C )}{s i n ( ∠ B A C + ∠ A B C )}

. With angle ABC = 110° - 35° = 75°, and using the sine rule for force resolution in the triangle formed by P and its components along AB and AC:

\frac{P}{s i n ( 110° )} = \frac{F _{A C}}{s i n ( 35° )}

. Thus

F_{A C} = \frac{100 \times 0.573}{0.939} \approx 61

JEE Main · 2021 · 16 Mar 2021 · Shift 1 · Integer answer

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JEE Main · 2021 · 16 Mar 2021 · Shift 1 · Vector

Solution

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