Find the torque due to three forces in Nm -3-2k- 4-2-3k- and -5k- acting on a particle at a point P 3-1-2 about the point A2-1-0-

Resultant force F=(î+3ĵ 2k̂)+ (4î+2ĵ 3k̂)+ ( î+ĵ 5k̂) F=4î+6ĵ 10k̂ N r=AP=î+2ĵ+2k̂ Thus, torque of resultant force about A is nbsp; nbsp;nbsp; τ = r×F =î ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Physics

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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
$\to τ = \to r \times \to F$ $= ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 1 & 2 & 2 4 & 6 & - 10 \end{matrix} ∣ ∣ ∣ ∣ ∣$ $= - 32^i + 18^j - 2^k Nm$

Suggest Corrections

Similar questions

Q. Find the shortest distance between the lines

¯ ¯ ¯ r = (4^i -^j) + λ (^i + 2^j - 3^k)

and

¯ ¯ ¯ r = (^i -^n j + 2^k) + μ (^i + 4^j - 5^k)

, where

λ

and

μ

are parameters.

Q. If

\to a = 2^i +^j +^k, \to b = 3^i - 4^j + 2^k, \to c =^i - 2^j + 2^k

then the projection of

\to a + \to b

\to c

Q. If

\to a = 2^i -^j +^k, \to b =^i + 2^j - 3^k, \to c = 3^i + μ^j + 5^k

are coplanar, then

μ

is a root of the equation

Q. If

¯ ¯¯ ¯ A = 2^i + 3^j -^k

and

¯ ¯¯ ¯ B = -^i + 3^j + 4^k

, then projection of

¯ ¯¯ ¯ A

¯ ¯¯ ¯ B

will be:

Q. If

\to a = 2^i +^j +^k, \to b = 5^i - 3^j +^k

, then orthogonal projection of

\to a

\to b

is -

Join BYJU'S Learning Program

Explore more

Intro to Torque

Standard XI Physics

Join BYJU'S Learning Program

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 $A (2, - 1, 0)$ .