Question

8. Two interfering wave (having intensities are 91 and 41) path difference between them is 11 2. The resultant intensity at this point will be (a) I (c) 4I (b) 91 (d) 251
explain in detail!​

Answer 1

Answer:

Given :

Which object has the greatest weight :

1.) Mass = 10 kg ; Gravitational field = 15 N/kg

2.) Mass = 15 kg ; Gravitational field = 13 N/kg

3.) Mass = 20 kg ; Gravitational field = 9 N/kg

4.) Mass = 50 kg ; Gravitational field = 3 N/kg

\begin{gathered}\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}}\end{gathered}\end{gathered}

To Find :

Object having greatest weight = ?

\begin{gathered}\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}}\end{gathered}\end{gathered}

Solution :

⚝ Formula Used :

\begin{gathered}\begin{gathered}\large{\color{cyan}{\bigstar}} \: \: {\underline{\boxed{\red{\sf{ Gravitational \: Field \: = \dfrac{Weight}{Mass}}}}}} \\ \\ \end{gathered}\end{gathered}

★

GravitationalField=

Mass

Weight

⚝ Let the Weights :

➙ {\sf{ W_1 = Weight \: of \: first \: Object }}➙ W

1

=WeightoffirstObject ➙ {\sf{ W_2 = Weight \: of \: second \: Object }} ➙W

2

=WeightofsecondObject ➙ {\sf{ W_3 = Weight \: of \: third \: Object }}➙W

3

=WeightofthirdObject ➙ {\sf{ W_4 = Weight \: of \: fourth \: Object }}➙ W

4

=WeightoffourthObject

\qquad{\rule{150pt}{1pt}}

⚝ Calculating the Weights :

\begin{gathered}\begin{gathered} \\ \\ \end{gathered}\end{gathered}

Weight of 1st Object :

\begin{gathered}\begin{gathered}{:\implies{\qquad{\sf{ Gravitational \: Field \: = \dfrac{Weight}{Mass}}}}} \\ \\ \ {:\implies{\qquad{\sf{ 15 = \dfrac{W_1}{10}}}}} \\ \\ \ {:\implies{\qquad{\sf{ W_1 = 15 \times 10 }}}} \\ \\ \ {\qquad{\textsf{ Weight of 1st Object = {\pink{\sf{150 \: N}}}}}}\end{gathered}\end{gathered}

:⟹GravitationalField=

Mass

Weight

:⟹15=

10

W

1

:⟹W

1

=15×10

Weight of 1st Object = 150 N

\begin{gathered}\begin{gathered} \\ \\ \end{gathered}\end{gathered}

Weight of 2nd Object :

\begin{gathered}\begin{gathered}{:\implies{\qquad{\sf{ Gravitational \: Field \: = \dfrac{Weight}{Mass}}}}} \\ \\ \ {:\implies{\qquad{\sf{ 13 = \dfrac{W_2}{15}}}}} \\ \\ \ {:\implies{\qquad{\sf{ W_2 = 13 \times 15 }}}} \\ \\ \ {\qquad{\textsf{ Weight of 2nd Object = {\purple{\sf{195 \: N}}}}}}\end{gathered}\end{gathered}

:⟹GravitationalField=

Mass

Weight

:⟹13=

15

W

2

:⟹W

2

=13×15

Weight of 2nd Object = 195 N

\begin{gathered}\begin{gathered} \\ \\ \end{gathered}\end{gathered}

Weight of 3rd Object :

\begin{gathered}\begin{gathered}{:\implies{\qquad{\sf{ Gravitational \: Field \: = \dfrac{Weight}{Mass}}}}} \\ \\ \ {:\implies{\qquad{\sf{ 9 = \dfrac{W_3}{20}}}}} \\ \\ \ {:\implies{\qquad{\sf{ W_3 = 9 \times 20 }}}} \\ \\ \ {\qquad{\textsf{ Weight of 3rd Object = {\pink{\sf{180 \: N}}}}}}\end{gathered}\end{gathered}

:⟹GravitationalField=

Mass

Weight

:⟹9=

20

W

3

:⟹W

3

=9×20

Weight of 3rd Object = 180 N

\begin{gathered}\begin{gathered} \\ \\ \end{gathered}\end{gathered}

Weight of 4th Object :

\begin{gathered}\begin{gathered}{:\implies{\qquad{\sf{ Gravitational \: Field \: = \dfrac{Weight}{Mass}}}}} \\ \\ \ {:\implies{\qquad{\sf{ 3 = \dfrac{W_4}{50}}}}} \\ \\ \ {:\implies{\qquad{\sf{ W_4 = 3 \times 50 }}}} \\ \\ \ {\qquad{\textsf{ Weight of 4th Object = {\purple{\sf{150 \: N}}}}}}\end{gathered}\end{gathered}

:⟹GravitationalField=

Mass

Weight

:⟹3=

50

W

4

:⟹W

4

=3×50

Weight of 4th Object = 150 N

\qquad{\rule{150pt}{1pt}}

⚝ Comparing the Weight :

\begin{gathered}\begin{gathered}\qquad \: {\sf{ W_1 = 150 \: N}} \\ \end{gathered}\end{gathered}

W

1

=150N

\begin{gathered}\begin{gathered}\qquad \: {\sf{ W_2 = 195 \: N}} \\ \end{gathered}\end{gathered}

W

2

=195N

\begin{gathered}\begin{gathered}\qquad \:{\sf{ W_3 = 180 \: N}} \\ \end{gathered}\end{gathered}

W

3

=180N

\begin{gathered}\begin{gathered}\qquad \:{\sf{ W_4 = 150 \: N}} \\ \\ \end{gathered}\end{gathered}

W

4

$7\begin{gathered}\begin{gathered}\qquad \:{\sf{ W_4 = 150 \: N}} \\ \\ \end{gathered}\end{gathered} </p><p>W </p><p>4$

=150N

Greatest : 195 N

\qquad{\rule{150pt}{1pt}}

⚝ Therefore :

❝ 2nd Object has the greatest weight (i.e, 195 N) . ❞

\begin{gathered}\begin{gathered} \\ {\underline{\colo

r{darkblue}{\rule{300pt}{9pt}}}}\end{gathered}\end{gathered}

Explanation:

\begin{gathered}\begin{gathered}\qquad \:{\sf{ W_4 = 150 \: N}} \\ \\ \end{gathered}\end{gathered}

W

4