If P → · Q → = P → · R → can we conclude that Q → = R → ?

Given, P → · Q → = P → · R → PQcosθ 1 = PRcosθ 2 Where θ 1 is smaller angle between P → & Q → and θ 2 is smaller angle between P → & R → Qcosθ 1 = Rcosθ 2 If θ 1 = θ 2 , then Q = R or Q → = R → If θ 1 ≠ θ 2 , then Q ≠ R or Q → ≠ R → Hence, it is the required solution.

A particle moves from position r → 1 = ( 2 i ^ + 3 j ^ - 4 k ^ ) m to position r → 2 = ( 7 i ^ + 8 j ^ + k ^ ) m under the action of a force F → = ( 2 i ^ + 2 j ^ - 2 k ^ ) newton. Calculate the work done

Given, Displacement vector r → 12 = r → 2 - r → 1 = ( 7 i ^ + 8 j ^ + k ^ ) - ( 2 i ^ + 3 j ^ - 4 k ^ ) = 5 i ^ + 5 j ^ + 5 k ^ Work done by constant force is given by W = F → · r → 12 = ( 5 i ^ + 5 j ^ + 5 k ^ ) · ( 2 i ^ + 2 j ^ - 2 k ^ ) = 10 + 10 - 10 = 10 J Hence, it is required answer.

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Gamma Question Bank for Medical Physics>Chapter 6 - Work, Energy and Power>Assignment>Q 20

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Earn 100

The momentum of a body is increased by $50 %$ . Find the percentage change in $K E$

Important Questions on Work, Energy and Power

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Gamma Question Bank for Medical Physics>Chapter 6 - Work, Energy and Power>Assignment>Q 21

If

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

can we conclude that

\vec{Q} = \vec{R} ?

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Gamma Question Bank for Medical Physics>Chapter 6 - Work, Energy and Power>Assignment>Q 22

A particle moves from position

{\vec{r}}_{1} = (2 \hat{i} + 3 \hat{j} - 4 \hat{k}) m

to position

{\vec{r}}_{2} = (7 \hat{i} + 8 \hat{j} + \hat{k}) m

under the action of a force

\vec{F} = (2 \hat{i} + 2 \hat{j} - 2 \hat{k})

newton. Calculate the work done

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Gamma Question Bank for Medical Physics>Chapter 6 - Work, Energy and Power>Assignment>Q 23

Can a body have energy without momentum?

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Gamma Question Bank for Medical Physics>Chapter 6 - Work, Energy and Power>Assignment>Q 24

Two springs

P

and

Q

are identical but

P

is harder than

Q (K_{p} > K_{Q})

. On which spring, more work will be done, if
(i) They are stretched by same force?
(ii) They are stretched through same distance?

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Gamma Question Bank for Medical Physics>Chapter 6 - Work, Energy and Power>Assignment>Q 25

What do you mean by zero work? State the conditions for zero work. Give one example.

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

Define work. State its dimensions, CGS & SI unit.

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

A bullet of mass

100 g

moving with a velocity of

300 m s^{- 1}

strikes a wall and goes out of the other side with a velocity of

100 m s^{- 1}

. Calculate work done in passing through the wall.

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

A bob of mass $m$ is suspended by a light string of length $l$ . It moves with horizontal velocity $v$ at the lowest point $A$ such that it completes a semicircular trajectory in the vertical plane with the string becoming slack only on reaching the top-most point $B$ . Show that minimum speed at $A$ should be $\sqrt{5 g l}$ .