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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

Let a force ...

Question

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.

(- 7^i + 3^j + 5^k) N m

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(- 11^i + 13^j + 15^k) N m

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

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(- 11^i + 3^j + 5^k) N m

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Solution

The correct option is B $(- 17^i + 13^j + 5^k) N m$
$\to t = \to r \times \to F = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 1 & - 1 & 6 2 & 3 & - 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$ $=^i (1 - 18) +^j (12 + 1) +^k (3 + 2)$
$\to t = (- 17^i + 13^j + 5^k) N - m$

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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

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.

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. Let

\to F

be the force acting on a particle having position vector

\to r

and

\to T

be the torque of this force about the origin. Then:

Q. Find the torque

(\to τ = \to r \times \to F)

of a force

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

acting at the point

\to r = 7^i + 3^j +^k

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The correct option is B (−17^i+13^j+5^k)Nm→t=→r×→F=∣∣ ∣ ∣∣^i^j^k1−1623−1∣∣ ∣ ∣∣=^i(1−18)+^j(12+1)+^k(3+2)→t=(−17^i+13^j+5^k)N−m

The correct option is B $(- 17^i + 13^j + 5^k) N m$
$\to t = \to r \times \to F = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 1 & - 1 & 6 2 & 3 & - 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$ $=^i (1 - 18) +^j (12 + 1) +^k (3 + 2)$
$\to t = (- 17^i + 13^j + 5^k) N - m$