Question

Question 7:
A force F = (2i+ 47N displaces the body by s = (3j + 5k)m in 2 s. Power generated will be
(A) 11 W
(B] 6 W
(C) 22. W
D) 12 W​

Answer 1

Solution :

⏭ Given:

✏ Force = (2i + 4j) N

✏ Displacement = (3j + 5k) m

✏ Time interval = 2s

⏭ To Find:

✏ Power generated

⏭ Concept:

✏ Power is defind as ratio of work done to the unit time.

⏭ Formula:

✏ Formula of power is given by

$\star \: \underline{ \boxed{ \bold{ \sf{ \pink{ \large{P = \frac{W}{t} = \frac{ \vec{F}{ \: \tiny{ \bullet}} \: \vec{S}}{t}}}}}}} \: \star$

⏭ Terms indication:

✏ P denotes power

✏ W denotes work done

✏ F denotes force

✏ S denotes displacement

✏ t denotes time

⏭ Calculation:

$\mapsto \sf \: P = \dfrac{(2 \hat{i} + 4 \hat{j}) \: {\tiny{ \bullet}}(3 \hat{j} + 5 \hat{k})}{2} \\ \\ \mapsto \sf \: P = \dfrac{12 \: ( \hat{j}{ \: \tiny{ \bullet}} \: \hat{j})}{2} \\ \\ \mapsto \sf \: P = \dfrac{12(1)}{2} \\ \\ \mapsto \: \underline{ \boxed{ \bold{ \sf{ \large{ \purple{Power = 6 \: Watt}}}}}} \: \gray{ \bigstar}$

⏭ Additional information:

• Power and work are scalar quantities.
• Force and displacement are vector quantities
• SI unit of power is J/s or Watt.