A door 1.6 m wide requires a minimum force of 1 N to be applied at the free end to open or close it. The minimum force that is required at a point 0.4 m away from the hinges for opening or closing the door is

Question

A door 1.6 m wide requires a minimum force of 1 N to be applied at the free end to open or close it. The minimum force that is required at a point 0.4 m away from the hinges for opening or closing the door is (A) 1.2 N (B) 2.4N (C) 3.6N (D) 4 N

Tardigrade Admin · Accepted Answer

The torque required in the initial case is, τ=1.6× 1=1.6Nm Now when the point of application of force is changed to, d=0.4m Hence, the force required will be, F=(τ/d)=(1 . 6/0 . 4)=4N will be the magnitude of force required to open or close the door.

Q. A door $1.6 m$ wide requires a minimum force of $1 N$ to be applied at the free end to open or close it. The minimum force that is required at a point $0.4 m$ away from the hinges for opening or closing the door is

$1.2 N$

$2.4 N$

$3.6 N$

$4 N$

The torque required in the initial case is,
$τ = 1.6 \times 1 = 1.6 N m$
Now when the point of application of force is changed to,
$d = 0.4 m$
Hence, the force required will be,
$F = \frac{τ}{d} = \frac{1.6}{0.4} = 4 N$ will be the magnitude of force required to open or close the door.

Q. A door 1.6m wide requires a minimum force of 1N to be applied at the free end to open or close it. The minimum force that is required at a point 0.4m away from the hinges for opening or closing the door is

1.2N

2.4N

3.6N

4N