If P → , Q → and R → Are non-zero vectors and P → · Q → = 0 and Q → · R → = 0 Then find P → · R →

P → · Q → = 0 ∴ P Q cos θ 1 = 0 or θ 1 = 90 ° Q → · R → = 0 ∴ Q R cos θ 2 = 0 or θ 2 = 90 ° Ad, these vectors are non-zero vector and if they are in same plane. Then, P → & R → Are parallel or antiparallel to each other. ∴ P → · R → = PRcos 0 ° = PR Or, P → · R → = PRcos 180 ° = - PR Hence, value of P → · R → is - PR Or PR .

A body moves from a point r → 1 = ( 2 i ^ + 3 j ^ ) to another point r → 2 = ( 3 i ^ + 2 j ^ ) due to force F → = 5 i ^ + 5 j ^ . Find the work done by the force.

Work done by any force is the dot product of force and displacement. We can get displacement by subtracting two position vectors. d → = displacement = r → 2 - r → 1 = i ^ - j ^ W = F → · d → = ( 5 i ^ + 5 j ^ ) · ( i ^ - j ^ ) = 5 - 5 = 0 Hence, work done by the force is 0 J .

E M B I B E

Gamma Question Bank for Medical Physics>Chapter 6 - Work, Energy and Power>Assignment>Q 26

EASY

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IMPORTANT

Earn 100

The dot product of two vectors is zero when the vectors are orthogonal and maximum when they are parallel to each other. Explain.

Important Questions on Work, Energy and Power

HARD

NEET

IMPORTANT

Gamma Question Bank for Medical Physics>Chapter 6 - Work, Energy and Power>Assignment>Q 27

Define scalar product of two vectors. Give its geometrical interpretation.

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Gamma Question Bank for Medical Physics>Chapter 6 - Work, Energy and Power>Assignment>Q 28

If

\vec{P}, \vec{Q}

and

\vec{R}

Are non-zero vectors and

\vec{P} \cdot \vec{Q} = 0

and

\vec{Q} \cdot \vec{R} = 0

Then find

\vec{P} \cdot \vec{R}

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Gamma Question Bank for Medical Physics>Chapter 6 - Work, Energy and Power>Assignment>Q 29

A body moves from a point

{\vec{r}}_{1} = (2 \hat{i} + 3 \hat{j})

to another point

{\vec{r}}_{2} = (3 \hat{i} + 2 \hat{j})

due to force

\vec{F} = 5 \hat{i} + 5 \hat{j} .

Find the work done by the force.

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IMPORTANT

Gamma Question Bank for Medical Physics>Chapter 6 - Work, Energy and Power>Assignment>Q 30

A uniform chain of length

l

And mass

m

Is lying on a smooth table and one-fourth of its length is hanging vertically over the edge of the table. Find the work needed to be done to pull the hanging part on to the table.

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Gamma Question Bank for Medical Physics>Chapter 6 - Work, Energy and Power>Assignment>Q 31

A man rowing a boat upstream is at rest w.r.t. the shore (i) Comment on the work done by him (ii) Is any work done by him when he stops rowing and moves along with the stream?

MEDIUM

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IMPORTANT

Gamma Question Bank for Medical Physics>Chapter 6 - Work, Energy and Power>Assignment>Q 32

Increase in