(D) The torque $\tau$ required to open or close the door is constant and is given by the product of the force $F$ and the distance $d$ from the hinge:

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(D) The torque $\tau$ required to open or close the door is constant and is given by the product of the force $F$ and the distance $d$ from the hinge: $\tau = F \times d$. Given that a force of $1 \,N$ is applied at the free end $(d = 1.6 \,m)$, the torque is $\tau = 1 \,N \times 1.6 \,m = 1.6 \,N-m$. To find the force $F'$ required at a distance $d' = 0.4 \,m$ from the hinges, we use the same torque: $F' = \frac{\tau}{d'} = \frac{1.6 \,N-m}{0.4 \,m} = 4 \,N$.

Class 11 Physics System of Particles and Rotational Motion Rotation Motion Basic, Motion of Connected Mass

Medium

$A$ door $1.6 \,m$ wide requires a force of $1 \,N$ to be applied at the free end to open or close it. The force that is required at a point $0.4 \,m$ distance from the hinges for opening or closing the door is (in $\,N$)

KCET 2009 All KCET

A
$1.2$
B
$3.6$
C
$2.4$
D
$4$

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System of Particles and Rotational Motion

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Rotation Motion Basic, Motion of Connected Mass

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$A$ door $1.6 \,m$ wide requires a force of $1 \,N$ to be applied at the free end to open or close it. The force that is required at a point $0.4 \,m$ distance from the hinges for opening or closing the door is (in $\,N$)

Similar Questions

For a particle,the angular velocity is $\vec{\omega} = \hat{i} - 2\hat{j} + 3\hat{k}$ and the position vector is $\vec{r} = \hat{i} + \hat{j} + \hat{k}$. What is the linear velocity $\vec{v}$?

$A$ block of mass $2\,kg$ hangs from the rim of a wheel of radius $0.5\,m$. On releasing from rest,the block falls through $5\,m$ height in $2\,s$. The moment of inertia of the wheel will be ...... $kg \cdot m^2$.

$A$ solid cylinder of mass $M$ and radius $R$ is placed in a horizontal position. Two strings are wrapped around the cylinder. Find the tension in the strings and the acceleration of the cylinder as the strings unwind.

$A$ plank with a uniform sphere placed on it rests on a smooth horizontal plane. The plank is pulled to the right by a constant force $F$. If the sphere does not slip over the plank,which of the following is true?

What is rotational motion and an axis of rotation?

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