Units and Measurements Test

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Units and Measurements Test - 85

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Weekly Quiz Competition

Question 1
1 / -0

A particle of mass $m$ collides with a stationary particle and continues to move at an angle of ${45}^{o}$ with respect to the original direction. The second particle also recoils at an angle of ${45}^{o}$ to this direction. The mass of the second particle is (collision is elastic)

A
$m$

B
$\sqrt { 2 } m$

C
$\cfrac { m }{ \sqrt { 2 } }$

D
$\cfrac { m }{ 2 }$

Solution
Question 2
1 / -0

Two resistors of resistances $R_1= 150\pm2 \space \Omega$ and $R_2 = 220\pm6 \space \Omega$ areconnected in parallel combination.Calculate the equivalent resistance.

A
$180\Omega$

B
$90\Omega$

C
$18\Omega$

D
$10\Omega$

Solution

$\text { Given }-R_{1}=150 \pm 2 \Omega \quad R_{2}=220 \pm 6 \Omega$
$\begin{array}{l} \text { When connect in Parallel we have - } \\ \qquad R_{e q}=\frac{R_{1} \cdot R_{2}}{R_{1}+R_{2}} \Rightarrow R_{e q}=\frac{150 \cdot 220}{150+220}=89.19 \mathrm{~s} \end{array}$
$\begin{array}{l} \text { for calculating error }- \\ \text { we have } \frac{1}{\operatorname{Req}}=\frac{1}{R_{1}}+\frac{1}{R_{2}} \end{array}$
$\begin{array}{l} \text { differentiate both Sides } \Rightarrow \\ \qquad-\frac{d\left(R_{e q}\right)}{\left(R_{e q}\right)^{2}}=-\frac{d R_{1}}{\left(R_{1}\right)^{2}}-\frac{d R_{2}}{\left(R_{2}\right)^{2}} \end{array}$
$\Rightarrow d(\text { R}_{eq})=(89.19)^{2} \cdot\left[\frac{2}{(150)^{2}}+\frac{6}{(220)^{2}}\right]$
$\begin{array}{l} d\left(R_{e q}\right)=1.69 \Omega \\ \text { Now we can write } R_{e q}=89.19 \pm 1.69 \Omega \\\Rightarrow \text{90}\Omega \text { can be be the maximum suitable answer. } \end{array}$
Question 3
1 / -0

Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii $R_1$ and $R_2$ respectively. The ratio of the mass of X to that of Y is?

A
$(R_1/R_2)^{1/2}$

B
$R_2/R_1$

C
$(R_1/R_2)^2$

D
$R_1/R_2$
Question 4
1 / -0

A body is dropped from a height h. If it acquired a momentum p, Then the mass of the body is

A
$\frac{P}{{\sqrt {2gh} }}$

B
$\frac{{{P^2}}}{{2gh}}$

C
$\frac{{2gh}}{{{P}}}$

D
$\sqrt {\frac{{2gh}}{p}}$
Question 5
1 / -0

A body of mass $m_1$ , moving with a uniform velocity of 50 $m{s^{ - 1}}$ collides with another body of mass $m_2$ at rest and then two together start moving with a velocity 40 $m{s^{ - 1}}$ . The ratio of their masses $\left( {\frac{{{m_1}}}{{{m_2}}}} \right)$ is

A
1 : 3

B
2 : 3

C
2 : 5

D
4 : 1

Solution
Question 6
1 / -0

Two particle X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii $R_1$ and $R_2$ respectively. The ratio of the mass X to the Y is:

A
${\left( {\frac{{{R_1}}}{{{R_2}}}} \right)^{\frac{1}{2}}}$

B
${\frac{{{R_2}}}{{{R_1}}}}$

C
${\left( {\frac{{{R_1}}}{{{R_2}}}} \right)^2}$

D
${\frac{{{R_1}}}{{{R_2}}}}$

Solution
Question 7
1 / -0

Which of the following quantity is dimension less?

A
Gravitational Constant

B
Plank's Constant

C
Power of lens

D
None of these

Solution
Question 8
1 / -0

van der Waal's constant $'a'$ has the dimensions of

A
$Mol \ {L}^{-1}$

B
$Atm\ {L}^{2}\ {mol}^{-2}$

C
$L\ {mol}^{-1}$

D
$Atm\ L\ {mol}^{-2}$

Solution
Question 9
1 / -0

The linear mass density i.e. mass per unit length of a rod of length L is given by $\rho$ = $\rho_{0}$ (1 + $\dfrac{x}{L}$ ), where $\rho_{0}$ is constant , x is distance from the left end. Find the c.o.m from the left end.

A
$\dfrac{5L}{9}$

B
$\dfrac{4L}{9}$

C
$\dfrac{5L}{8}$

D
$\dfrac{3L}{8}$
Question 10
1 / -0

Two isotopes of an element $X$ are present in the ratio of $1:2$ , having mass number $M$ and ( $M+0.5$ ) respectively. Find the mean mass number of $X$

A
$M + (2/3)$

B
$M + (1/3)$

C
$M + (1/4)$

D
$M + 3$

Solution

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Re-Attempt Weekly Quiz Competition

Units and Measurements Test - 85

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Units and Measurements Test - 85

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Question 1

mmm

2m\sqrt { 2 } m2​m

m2\cfrac { m }{ \sqrt { 2 } } 2​m​

m2\cfrac { m }{ 2 } 2m​

Solution

Question 2

180Ω180\Omega180Ω

90Ω90\Omega90Ω

18Ω18\Omega18Ω

10Ω10\Omega10Ω

Solution

Question 3

(R1/R2)1/2(R_1/R_2)^{1/2}(R1​/R2​)1/2

R2/R1R_2/R_1R2​/R1​

(R1/R2)2(R_1/R_2)^2(R1​/R2​)2

R1/R2R_1/R_2R1​/R2​

Question 4

P2gh\frac{P}{{\sqrt {2gh} }}2gh​P​

P22gh\frac{{{P^2}}}{{2gh}}2ghP2​

2ghP\frac{{2gh}}{{{P}}}P2gh​

2ghp\sqrt {\frac{{2gh}}{p}} p2gh​​

Question 5

1 : 3

2 : 3

2 : 5

4 : 1

Solution

Question 6

(R1R2)12{\left( {\frac{{{R_1}}}{{{R_2}}}} \right)^{\frac{1}{2}}}(R2​R1​​)21​

R2R1{\frac{{{R_2}}}{{{R_1}}}}R1​R2​​

(R1R2)2{\left( {\frac{{{R_1}}}{{{R_2}}}} \right)^2}(R2​R1​​)2

R1R2{\frac{{{R_1}}}{{{R_2}}}}R2​R1​​

Solution

Question 7

Gravitational Constant

Plank's Constant

Power of lens

None of these

Solution

Question 8

Mol L−1Mol \ {L}^{-1}Mol L−1

Atm L2 mol−2Atm\ {L}^{2}\ {mol}^{-2}Atm L2 mol−2

L mol−1L\ {mol}^{-1}L mol−1

Atm L mol−2Atm\ L\ {mol}^{-2}Atm L mol−2

Solution

Question 9

5L9\dfrac{5L}{9}95L​

4L9\dfrac{4L}{9}94L​

5L8\dfrac{5L}{8}85L​

3L8\dfrac{3L}{8}83L​

Question 10

M+(2/3)M + (2/3)M+(2/3)

M+(1/3)M + (1/3)M+(1/3)

M+(1/4)M + (1/4)M+(1/4)

M+3M + 3M+3

Solution

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$m$

$\sqrt { 2 } m$

$\cfrac { m }{ \sqrt { 2 } }$

$\cfrac { m }{ 2 }$

$180\Omega$

$90\Omega$

$18\Omega$

$10\Omega$

$(R_1/R_2)^{1/2}$

$R_2/R_1$

$(R_1/R_2)^2$

$R_1/R_2$

$\frac{P}{{\sqrt {2gh} }}$

$\frac{{{P^2}}}{{2gh}}$

$\frac{{2gh}}{{{P}}}$

$\sqrt {\frac{{2gh}}{p}}$

${\left( {\frac{{{R_1}}}{{{R_2}}}} \right)^{\frac{1}{2}}}$

${\frac{{{R_2}}}{{{R_1}}}}$

${\left( {\frac{{{R_1}}}{{{R_2}}}} \right)^2}$

${\frac{{{R_1}}}{{{R_2}}}}$

$Mol \ {L}^{-1}$

$Atm\ {L}^{2}\ {mol}^{-2}$

$L\ {mol}^{-1}$

$Atm\ L\ {mol}^{-2}$

$\dfrac{5L}{9}$

$\dfrac{4L}{9}$

$\dfrac{5L}{8}$

$\dfrac{3L}{8}$

$M + (2/3)$

$M + (1/3)$

$M + (1/4)$

$M + 3$