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Intro to Torque

Find the torq...

Question

Find the torque due to three forces (in $Nm$ ) $^i + 3^j - 2^k$ , $4^i + 2^j - 3^k$ and $-^i +^j - 5^k$ acting on a particle at a point $P (3, 1, 2)$ about the point $A (2, - 1, 0)$ .

- 2^i - 32^j - 14^k Nm

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- 32^i + 18^j - 2^k Nm

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32^i + 2^j + 14^k Nm

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- 32^i + 2^j - 14^k Nm

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Solution

The correct option is B $- 32^i + 18^j - 2^k Nm$
Resultant force $\to F = (^i + 3^j - 2^k) + (4^i + 2^j - 3^k) + (-^i +^j - 5^k)$
$\to F = 4^i + 6^j - 10^k N$
$\to r = A P =^i + 2^j + 2^k$
Thus, torque of resultant force about $A$ is
$\to τ = \to r \times \to F$ $= ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 1 & 2 & 2 4 & 6 & - 10 \end{matrix} ∣ ∣ ∣ ∣ ∣$ $= - 32^i + 18^j - 2^k Nm$

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Similar questions

Q. A force

\to F = 4^i - 5^j + 3^k

is acting at point

_{1} =^i + 2^j + 3^k

. The torque acting about the point

_{2} = 3^i - 2^j - 3^k

The Vector $- - \to O A = - 2^i +^j + 2^k$ is rotated through an angle $90^{\circ}$ about origin (O)In new Position it passes through $^i +^k$ . Then the vector in new position is

Q. A force

\to F = 4^i - 5^j + 3^k

is acting a point

_{1} =^i + 2^j + 3^k

. The torque acting about a point

_{2} = 3^i - 2^j - 3^k

Q. A force

\to F = 4^i - 5^j + 3^k

is acting at a point

_{1} =^i - 2^j + 3^k

. Find the torque acting about a point

_{2} = 3^i - 2^j - 3^k

Q. Constant forces

\to P =^i - 2^j + 3^k, \to Q = -^i + 3^j -^k

and

\to R = 2^i - 4^j + 3^k

act on a particle. The work done when the particle is displaced from a point

A

with position vector

4^i - 3^j - 2^k

to the point

B

with position vector

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Intro to Torque

Standard XII Physics

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Find the torque due to three forces (in Nm) ^i+3^j−2^k, 4^i+2^j−3^k and −^i+^j−5^k acting on a particle at a point P(3,1,2) about the point A(2,−1,0).

The correct option is B −32^i+18^j−2^k Nm Resultant force →F=(^i+3^j−2^k)+(4^i+2^j−3^k)+(−^i+^j−5^k) →F=4^i+6^j−10^k N →r=AP=^i+2^j+2^k Thus, torque of resultant force about A is →τ=→r×→F =∣∣ ∣ ∣∣^i^j^k12246−10∣∣ ∣ ∣∣ =−32^i+18^j−2^k Nm

Find the torque due to three forces (in $Nm$ ) $^i + 3^j - 2^k$ , $4^i + 2^j - 3^k$ and $-^i +^j - 5^k$ acting on a particle at a point $P (3, 1, 2)$ about the point $A (2, - 1, 0)$ .