Solveeit Logo
Login

Question

Question: Figure shows a lamina in *x-y* plane. Two axes z and *z’* pass perpendicular to its plane. A force F...

Figure shows a lamina in x-y plane. Two axes z and z’ pass perpendicular to its plane. A force F acts in the plane of lamina at point P as shown. Which of the following statements is incorrect?

(The point P is closer to z′z' -axis than the z- axis).

A

Torque τ\taucaused by F about z axis is along k^\widehat{k}

B

Torque τ′\tau' caused by F about z’ axis is along –k^\widehat{k}

C

Torque caused by F about z axis is greater in magnitude than that about z’ axis.

D

Total torque is given by τ=τ+τ′\tau = \tau + \tau'

Answer

Total torque is given by τ=τ+τ′\tau = \tau + \tau'

Explanation

Solution

The directions of τ→\overset{\rightarrow}{\tau} is given by right handed screw rule.

According to this rule, the directions of τ→\overset{\rightarrow}{\tau} caused by F→\overset{\rightarrow}{F}about z axis is along k^.\widehat{k}.

Hence, options (1) is correct.

Again, according to this rule, the directions of τ→\overset{\rightarrow}{\tau} caused by F→\overset{\rightarrow}{F} about z axis is along −k^.- \widehat{k}.

Hence ,option (2) is correct.

As τ→=r→×F→\overset{\rightarrow}{\tau} = \overset{\rightarrow}{r} \times \overset{\rightarrow}{F}and P is closer z` axis, therefore τ→\overset{\rightarrow}{\tau} caused by F→\overset{\rightarrow}{F}about z axis is greater in magnitude than that about z` axis.

Hence option (3) is also correct.

It is meaningless to add torques about two different axes.

Hence, options (4) is incorrect.