The torque of a force \(5\^{i}+3\^{j}−7\^{k}\) about the origin is τ. If the force acts on a particle whose position vector is\( 2\^{i}+2\^{j}+\^{k}\), then the value of τ will be
The torque of a force \(5\^{i}+3\^{j}−7\^{k}\) about the origin is τ. If the force acts on a particle whose position vector is\( 2\^{i}+2\^{j}+\^{k}\), then the value of τ will be
- \(11\^{i}+19\^{j}−4\^{k}\)
- \(-11\^{i}+9\^{j}−16\^{k}\)
- \(-17\^{i}+19\^{j}−4\^{k}\)
- \(17\^{i}+9\^{j}+16\^{k}\)
The Correct Option is C
Solution and Explanation
\(\begin{bmatrix} \^{i} & \^{j} & \^{k}\\ 2 & 2 &1 \\ 5& 3 & -7 \end{bmatrix}\)
\(=\^{i}(−14−3)+\^{j}(5+14)+\^{k}(6−10)\)
\(=−17\^{i}+19\^{j}−4\^{k}\)
So, the correct option is (C): \(=−17\^{i}+19\^{j}−4\^{k}\)
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Concepts Used:
Intermolecular Forces
The attractive and repulsive forces that arise between the molecules of a substance are termed as the intermolecular forces. These forces are responsible for the physical and chemical properties of the matter. Intermolecular forces or IMF are also known as the electrostatic forces between molecules and atoms.
Intermolecular forces exist between the molecules and affect the physical properties of a substance. The intermolecular forces of attraction are the result of the reaction between the protons or positive compounds and the electrons or negative compounds of a molecule.
Intermolecular forces examples: - Ion-dipole forces, ion-induced dipole forces, and hydrogen bonding.
The intermolecular forces depend on the following interactions:
- Dipole-Dipole Interactions
- Ion-Dipole Interactions
- Ion Induced Dipole Interactions
- Dipole Induced Dipole Interaction
- Dispersion Forces or London Forces