Suppose that a rigid body is free to rotate about a fixed point O- If a force F acts on the body at a point P- then the body will tend to rotate about an axis through O- This effect is measured by the torque vector t which is given by t-r- Fwhere r is the position vector OP- The straight line through O determined by t is the axis of rotation- The vector r- F and T form a right handed system-The magnitude of the torque exerted at origin by the force F - i - 2j - k at the point 1- 1- 1 is

The correct option is D √(2) Here F⃗=î+2ĵ+k̂ OP=r⃗=î+ĵ+k̂ t=r× F t=î amp;ĵ amp;k̂ 1 amp;1 amp;1 1 amp;2 amp;1 ...

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Byju's Answer

Standard XII

Physics

Intro to Torque

Suppose that ...

Question

Suppose that a rigid body is free to rotate about a fixed point $O$ . If a force $F$ acts on the body at a point $P$ , then the body will tend to rotate about an axis through $O$ . This effect is measured by the torque vector $t$ which is given by $t = r \times F$
where $r$ is the position vector $O P$ . The straight line through $O$ determined by $t$ is the axis of rotation. The vector $r, F$ and $T$ form a right handed system.
The magnitude of the torque exerted at origin by the force $F = i + 2 j + k$ at the point $(1, 1, 1)$ is

1

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\sqrt{5}

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\sqrt{3}

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\sqrt{2}

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Solution

The correct option is D $\sqrt{2}$
Here
$\to F =^i + 2^j +^k$
$O P = \to r =^i +^j +^k$
$t = r \times F$
$t = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 1 & 1 & 1 1 & 2 & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$
$t =^i (- 1) -^j (0) +^k (2 - 1)$
$t = -^i +^k$
Magnitude
$| t | = \sqrt{1^{2} + 1^{2}}$
$| t | = \sqrt{2}$

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The correct option is D √2Here →F=^i+2^j+^kOP=→r=^i+^j+^kt=r×Ft=∣∣ ∣ ∣∣^i^j^k111121∣∣ ∣ ∣∣t=^i(−1)−^j(0)+^k(2−1)t=−^i+^kMagnitude |t|=√12+12|t|=√2