Question

A: Torque on a body can be zero even if there is a net force on it. R: Torque and force on a body are always perpendicular.

A: A couple does not exert a net force even though it exerts a torque. R: Couple is a pair of two forces with equal magnitude but opposite directions acting simultaneously on a body in different lines of action.

A: To unscrew a rusted nut, we need a pipe wrench of longer arm. R: Wrench with longer arm reduces the force applied on arm.

The cross product of two vectors is given by Vector C = A × B. The magnitude of the vector defined from cross product of two vectors is equal to product of magnitudes of the vectors and sine of angle between the vectors. Direction of the vectors is given by right hand corkscrew rule and is perpendicular to the plane containing the vectors. ∴ |vector C| = ABsinθ and Vector C = ABsinθ n Where, cap n is the unit vector perpendicular to the plane containing the vectors A and B. Following are properties of vector product: a) Cross product does not obey commutative law. But its magnitude obeys commutative low. b) It obeys distributive law c) The magnitude cross product of two vectors which are parallel is zero. Since θ = 0; vector |A x B| = AB sin 0° = 0 d) For perpendicular vectors, θ = 90°, vector |A x B| = AB sin 90° |cap n| = AB î x î = ĵ x ĵ = ƙ x ƙ = 0 î x ĵ = ƙ; ĵ x ƙ = î; ƙ x î = ĵ ĵ x î = -(î x ĵ) = -ƙ; ƙ x ĵ = -(ĵ x ƙ) = -î; î x ƙ = -(ƙ x î) = -ĵ