Let a force F be acting on a body free to rotate about a point O and let r be the position vector of any point P on the line of action of the force- Then torque t of this force about point O is defined as -T - r - FGiven- F -2 -3 -k- N and r -6 k- m- Find the torque of this force-A- -17 -13 -5 k- N mB- -17 -13 -10 k- N mC- -17 -13 -5 k- N mD- 17 -13 -5 k- Nm

The correct option is A ( 17î+13ĵ+5k̂) Nmτ=r×F=[ î amp;ĵ amp; k̂; 1 amp; 1 amp; 6; 2 amp; 3 amp; 1 ] = î(1 18) ĵ( 1 12)+k̂(3+2) =( 17î ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

Let a force F...

Question

Let a force $\to F$ be acting on a body free to rotate about a point $O$ and let $\to r$ be the position vector of any point $P$ on the line of action of the force. Then torque $\to τ$ of this force about point $O$ is defined as :
$\to τ = \to r \times \to F$
Given, $\to F = (2^i + 3^j -^k) N$ and $\to r = (^i -^j + 6^k) m$ . Find the torque of this force.

(- 17^i + 13^j + 5^k) N m

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(17^i + 13^j + 5^k) N m

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(- 17^i - 13^j + 5^k) N m

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(- 17^i + 13^j + 10^k) N m

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Solution

The correct option is A $(- 17^i + 13^j + 5^k) N m$
$\to τ = \to r \times \to F = ⎡ ⎢ ⎣ \begin{matrix} ^i & ^j & ^k 1 & - 1 & 6 2 & 3 & - 1 \end{matrix} ⎤ ⎥ ⎦$
$=^i (1 - 18) -^j (- 1 - 12) +^k (3 + 2)$
$= (- 17^i + 13^j + 5^k) N m$

Suggest Corrections

Similar questions

Q. Let a force

\to F

be acting on a body free to rotate about a point

O

and let

\to r

be the position vector of any point

P

on the line of action of the force. Then torque

\to τ

of this force about point

O

is defined as :

\to τ = \to r \times \to F

Given,

\to F = (2^i + 3^j -^k) N

and

\to r = (^i -^j + 6^k) m

. Find the torque of this force.

Q. Let a force

\to F

be acting on a body free to rotate about a point O and let

\to r

the position vector of any point P on the line of action of the force. Then torque

\to t

of this force about point O is defined as

\to t = \to r \times \to F

Given,

\to F = (2^i + 3^j -^k) N a n d \to r = (^i -^j + 6^k) m

Find the torque of this force.

Choose the correct option for the two given statements from the options:

Statement-

1

: The torque about the point

2^i +^j -^k

of a force represented by

4^i +^k

acting through the point

^i -^j + 2^k

- 2^i + 13^j + 8^k

Statement-

2

: The torque of a force

\to F

about a point

P

\to r \times \to F

where

\to r

is the vector from the point

P

to any point

\to a

on the line of action

L

\to F

Q. A force

\to F = (^i -^j +^k) N

acts at point

P

. Find the torque due to the force

\to F

about

O

Q. 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)

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The correct option is A (−17^i+13^j+5^k) Nm→τ=→r×→F=⎡⎢⎣^i^j^k1−1623−1⎤⎥⎦ =^i(1−18)−^j(−1−12)+^k(3+2) =(−17^i+13^j+5^k)Nm

The correct option is A $(- 17^i + 13^j + 5^k) N m$
$\to τ = \to r \times \to F = ⎡ ⎢ ⎣ \begin{matrix} ^i & ^j & ^k 1 & - 1 & 6 2 & 3 & - 1 \end{matrix} ⎤ ⎥ ⎦$
$=^i (1 - 18) -^j (- 1 - 12) +^k (3 + 2)$
$= (- 17^i + 13^j + 5^k) N m$