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Pearson IIT Foundation class 6 physics - chapter 1
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Answer 1

Answer:

Work is defined as the dot product of force and displacement. The unit of work is joule.

Explanation:

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Answer 2

Question:

⋆ Find the unit of work if work is the product of force and displacement, force = mass × acceleration, where acceleration = length/time².

Provided that:

• Work is the product of force and displacement.

• Force = mass × acceleration, where acceleration = length/time².

To determine:

• The unit of work.

Solution:

• The unit of work = Nm / Joules

Required solution:

Focus point: Work is the product of force and displacement. Meanforth,

• Work = Force × Displacement

Also provided that:

Force is the product of mass and acceleration. Henceforth,

• Force = Mass × Acceleration

We know that,

Acceleration is the change in velocity with respect to time.

• ${\sf{a \: = \dfrac{v-u}{t}}}$

(Where, a denotes acceleration, v denotes final velocity, u denotes initial velocity and t denotes time taken.)

____________________________

Knowledge required:

• SI unit of velocity is m/s.
• SI unit of time is second.
• SI unit of mass is kg.
• SI unit of displacement is m

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~ Now let us find out the SI unit of acceleration by using its defination and formula. Let's do it!

${\sf{:\implies a \: = \dfrac{v-u}{t}}}$

${\sf{:\implies a \: = \dfrac{Change \: in \: velocity}{Time}}}$

${\sf{:\implies a \: = \dfrac{m/s}{s}}}$

${\sf{:\implies a \: = \dfrac{m}{s^2}}}$

• Therefore, SI unit of acceleration must be m/s².

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~ Now let us know find out the SI unit of force by using its defination and formula. Let's do it!

${\sf{:\implies F \: = ma}}$

${\sf{:\implies Force \: = mass \times acceleration}}$

${\sf{:\implies Force \: = kg \times m/s^2}}$

${\sf{:\implies Force \: = kg \: m/s^2}}$

• Henceforth, SI unit of force must be kg m/s².

• But to honour to “Sir Issac Newton” the SI unit of force is denotes as Newton(N).

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~ Now let us find out the SI unit of work by using its defination and formula. Let's do it too!

${\sf{:\implies Work \: = Force \times Displacement}}$

${\sf{:\implies W \: = Fs}}$

${\sf{:\implies W \: = kg \: m/s^2 \times m}}$

${\sf{:\implies W \: = Newton \times metres}}$

${\sf{:\implies W \: = N \times m}}$

${\sf{:\implies W \: = Nm}}$

• Henceforth, SI unit of work is Nm that is Newton metre.

• But to the honour of “Sir James Prescott Joule” SI unit of work done is said to we Joules(J).

Additional information:

About work:

➟ Work - If a body get displaced when a force acts on it, work it said to be done. Work is measured by the product of force and displacement of the body along the direction of force. If a body get displaced by s when a force f act's on it, then the work w be ${\small{\underline{\boxed{\sf{Fs \: cos \theta}}}}}$

(Where, θ denotes angle between force and displacement)

⋆ If both force and displacement are in the same direction, then W = Fs.

About acceleration:

$\begin{gathered}\boxed{\begin{array}{c}\\ \bf What \: is \: acceleration? \\ \\ \sf The \: rate \: of \: change \: of \: velocity \: of \: an \\ \sf object \: with \: respect \: to \: time \\ \sf is \: known \: as \: acceleration. \\ \\ \sf \star \: Negative \: acceleration is \: known \: as \: deacceleration. \\ \sf \star \: Deacceleration \: is \: known \: as \: retardation. \\ \sf \star \: It's \: SI \: unit \: is \: ms^{-2} \: or \: m/s^2 \\ \sf \star \: It \: may \: be \: \pm ve \: or \: 0 \: too \\ \sf \star \: It \: is \: a \: vector \: quantity \\ \\ \bf Conditions \: of \pm ve \: or \: 0 \: acceleration \\ \\ \sf \odot \: Positive \: acceleration: \: \sf When \: \bf{u} \: \sf is \: lower \: than \: \bf{v} \\ \sf \odot \: Negative \: acceleration: \: \sf When \: \bf{v} \: \sf is \: lower \: than \: \bf{u} \\ \sf \odot \: Zero \: acceleration: \: \sf When \: \bf{v} \: \sf and \: \bf{u} \: \sf are \: equal \end{array}}\end{gathered}$

About velocity:

Velocity = Velocity of moving object is defined as the displacement of the object in unit time interval i.e., velocity = Displacement/Time. It's vector quantity and it's SI unit is metre/second.

About displacement:

Displacement = Shortest distance covered by a body in a definite direction is called displacement.

→ Displacement may be positive, negative or zero whereas distance is always positive.

→ Distance is a scaler quantity whereas displacement is a vector quantity both having the same unit.

→ In general magnitude of displacement ≤ Distance