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Class 12th Physics NCERT Exemplar Solutions Class 12th Chapter Seven

Two bodies of mass 1kg and 3kg have position vectors $\hat{i} + 2 \hat{j} + \hat{k} a n d - 3 \hat{i} - 2 \hat{j} + \hat{k}$ respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector:

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Vishal Baghel

Contributor-Level 10

$m_{1} = 1 k g, {\vec{r}}_{1} = \hat{i} + 2 \hat{j} + \hat{k}$

$m_{1} = 3 k g, {\vec{r}}_{2} = - 3 \hat{i} - 2 \hat{j} + \hat{k}$

${\vec{r}}_{c o m} = \frac{m_{1} {\vec{r}}_{1} + m_{2} {\vec{r}}_{2}}{m_{1} + m_{2}} = \frac{1}{4} (\hat{i} + 2 \hat{j} + \hat{k} + - 9 \hat{i} - 6 \hat{j} + 3 \hat{k})$

= $2 \hat{i} - \hat{j} + \hat{k}$

$| {\vec{r}}_{c o m} | = \sqrt[]{4 + 1 + 1} = \sqrt[]{6 .}$

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Class 12th Motion in a Plane

A ball is projected with kinetic energy E, at an angle of 60° to the horizontal. The kinetic energy of this ball at the highest point of its flight will become:

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Vishal Baghel

Contributor-Level 10

$E = \frac{1}{2} m u^{2}$

$E_{H i g h e s t p o i n t} = \frac{1}{2} m {(\frac{u}{2})}^{2} = \frac{1}{8} m u^{2} = \frac{E}{4}$

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Class 12th Physics NCERT Exemplar Solutions Class 12th Chapter Ten

A cube of metal is subjected to a hydrostatic pressure 4GPa. The percentage change in the length of the side of the cube is close to: (Given bulk modulus of metal, $B = 8 * 10^{10}$ $P a)$

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alok kumar singh

Contributor-Level 10

Sol.

$\begin{array}{r} \end{array}$ $\begin{array}{r} ↑_{1}^{?} (1) ε = 3 \\ (2) ε - I r = 2.5 V \\ \Rightarrow I r = 0.5 \\ Now, IR = 2.5 \\ \Rightarrow \frac{R}{r} = 5 . \\ \Rightarrow \frac{P_{R}}{R_{r}} = \frac{I^{2} R}{I^{2} r} = \frac{R}{r} = 5 \\ \Rightarrow P_{r} = \frac{0.5}{5} = 0.1 \end{array}$

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Class 12th Physics NCERT Exemplar Solutions Class 12th Chapter Four

A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a speed v. Which of the following curve represents the correct relation between the normal reaction on the block by the wall (N) and speed of the block (v)?

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Vishal Baghel

Contributor-Level 10

$N = \frac{m v^{2}}{R}$

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Class 12th Conic Sections

The number of points of intersection of $| z - (4 + 3 i) | = 2 a n d | z | + | z - 4 | = 6, z \in C,$ is

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Payal Gupta

Contributor-Level 10

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Class 12th Physics NCERT Exemplar Solutions Class 12th Chapter Three

If t = $\sqrt[]{x} + 4, t h e n {(\frac{d x}{d t})}_{t = 4} i s :$

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Vishal Baghel

Contributor-Level 10

$t = \sqrt[]{x} + 4$

then $\frac{d t}{d x} = \frac{1}{2 \sqrt[]{x}} ∴ {(\frac{d x}{d t})}_{t = 4} = {(2 \sqrt[]{x})}_{t = 4} = {[2 (t - 4)]}_{a t t = 4}$

= 0

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Class 12th Physics NCERT Exemplar Solutions Class 12th Chapter Six

Match the thermodynamics processes taking place in a system with the correct conditions. In the table: $Δ Q$ is the heat supplied, $Δ W$ is the work done and $Δ U$ is change in internal energy of the system. Match the following:

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alok kumar singh

Contributor-Level 10

Sol. $? v$

$\Rightarrow m v = 16 {m v}_{1}$

$\Rightarrow V_{1} = \frac{V}{16}$

$\Rightarrow Δ k$ loss $= \frac{1}{2} {m v}^{2} - \frac{1}{2} (16 m) {(\frac{V}{16})}^{2}$

$\Rightarrow \frac{1}{2} {m v}^{2} (\frac{15}{16})$

$%$ loss $= \frac{15}{16} * 100 = 93.75 %$

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Class 12th Physics NCERT Exemplar Solutions Class 12th Chapter Three

A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height $\frac{h}{3}$ while going up and coming down respectively.

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Vishal Baghel

Contributor-Level 10

$h = \frac{u^{2}}{2 g} \Rightarrow u = \sqrt[]{2 g h}$

$\frac{h}{3} = \sqrt[]{2 g h} t - 5 t^{2}$

$5 t^{2} - \sqrt[]{20 h} t + \frac{h}{3} = 0$

$t = \frac{\sqrt[]{20 h} \pm \sqrt[]{20 h - 4 * 5 * \frac{h}{3}}}{10}$

$∴ \frac{t_{1}}{t_{2}} = \frac{\sqrt[]{20 h} - \sqrt[]{\frac{40}{3} h}}{\sqrt[]{20 h} + \sqrt[]{\frac{40}{3} h}} = \frac{1 - \sqrt[]{\frac{2}{3}}}{1 + \sqrt[]{\frac{2}{3}}} = \frac{\sqrt[]{3} - \sqrt[]{2}}{\sqrt[]{3} + \sqrt[]{2}}$

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