Show that the vectors A → = 2 i ^ - 3 J ^ - k ~ and B → = - 6 i ^ + 9 j ^ + 3 k ^ are parallel.

Given a vector A → = 2 i ^ - 3 J ^ - k ~ . and B → = - 6 i ^ + 9 j ^ + 3 k ^ . As we know that A → × B → = ABsin θ . If these vectors are parallel then the angle between them will be zero. So the value of their cross product should be zero. Here we have, A → × B → = i ^ j ^ k ^ 2 - 3 - 1 - 6 9 3 = i ^ - 3 × 3 - - 1 × 9 + j ^ ( - 1 ) × 6 - 2 × 3 + k ^ ( 2 × 9 ) - - 3 - 6 = i ^ ( - 9 + 9 ) + j ^ ( 6 - 6 ) + k ^ ( 18 - 18 ) = 0 . So we get that AB sinθ = 0 . since A ≠ 0 , B ≠ 0 , so sinθ = 0 or θ = 0 . Since the angle between the vectors is zero, hence these vectors are parallel.

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Gamma Question Bank for Medical Physics>Chapter 7 - System of Particles and Rotational Motion>Assignment>Q 12

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Rotational energy of a rigid body of moment of inertia $I$ rotating with angular velocity $ω$ about a fixed axis is $\frac{1}{2} I ω^{2}$ .

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Important Questions on System of Particles and Rotational Motion

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Gamma Question Bank for Medical Physics>Chapter 7 - System of Particles and Rotational Motion>Assignment>Q 13

Moment of inertia of a hollow cylinder of mass

M

and radius

R

about the axis of cylinder is _____

R^{2}

.

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Gamma Question Bank for Medical Physics>Chapter 7 - System of Particles and Rotational Motion>Assignment>Q 5

A body rolls down on an inclined plane. If its kinetic energy of rotational motion is

40 %

of its kinetic energy of translational motion, then the body is

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Gamma Question Bank for Medical Physics>Chapter 7 - System of Particles and Rotational Motion>Assignment>Q 6

\vec{a} \times (\vec{b} + \vec{c}) =

\vec{a} \times \vec{b}

_____

\vec{a} \times \vec{c}

.

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Gamma Question Bank for Medical Physics>Chapter 7 - System of Particles and Rotational Motion>Assignment>Q 8

Flywheel have _____ moment of inertia. (large/small)

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Gamma Question Bank for Medical Physics>Chapter 7 - System of Particles and Rotational Motion>Assignment>Q 23

Show that the vectors $\vec{A} = 2 \hat{i} - 3 \hat{J} - \tilde{k}$ and $\vec{B} = - 6 \hat{i} + 9 \hat{j} + 3 \hat{k}$ are parallel.

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Gamma Question Bank for Medical Physics>Chapter 7 - System of Particles and Rotational Motion>Assignment>Q 1

Three point masses $m_{1}, m_{2}$ and $m_{3}$ are placed at the corners of a thin massless rectangular sheet $(1.2 m \times 1.0 m)$ as shown. Centre of mass will be located at the point

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Gamma Question Bank for Medical Physics>Chapter 7 - System of Particles and Rotational Motion>Assignment>Q 2

Figure shows a composite system of two uniform rods of lengths as indicated. Then the coordinates of the centre of mass of the system of rods are

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Gamma Question Bank for Medical Physics>Chapter 7 - System of Particles and Rotational Motion>Assignment>Q 3

A circular plate of diameter $' a'$ is kept in contact with a square plate of side $a$ as shown. The density of the material and the thickness are same everywhere. The centre of mass of composite system will be

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