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TEST SERIES (PHYSICS FST)

266226 The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant $k$ and compresses it by length $L$ . The maximum velocity of the block after collision is:

1 Zero

2

\sqrt{\frac{2 k}{m}} L

3

\sqrt{\frac{k}{m}} L

4

\sqrt{M MLL}

Explanation:

c
When block of mass $M$ collides with the spring its kinetic energy gets converted into elastic potential energy of the spring
From the law of conservation of energy
$\frac{1}{2} M v^{2} = \frac{1}{2} K L^{2} \Rightarrow v = \sqrt{\frac{K}{M}}$

**NCERT-XI-I-81**

TEST SERIES (PHYSICS FST)

266227 Assertion: The temperature at which Centigrade and Fahrenheit thermometers read the same is $- 60^{\circ}$ . Reas on: There is no relation between Fahrenheit and Centigrade temperature.

1 Both assertion and reason are true and the reason is the correct explanation of the assertion

2 Both assertion and reason are true but reason is not the correct explanation of the assertion

3 Assertion is true but reason is false

4 Assertion and reason both are false

Explanation:

d
The relation between F and Cscale is, $\frac{C}{5} = \frac{F - 32}{9}$ . If $F = C \Rightarrow C = - 40^{\circ} C$ , i.e., at $- 40^{\circ}$ the Centigrade and Fahrenheit thermometers reads the same.

**NCERT-XI-II-203**

TEST SERIES (PHYSICS FST)

266228 The moment of inertia of $a$ thin uniform rod rotating about the perpendicular axis passing through one end is $I$ . The same rod is bent into a ring and its moment of inertia about the diameter is $I^{'}$ , then the ratio $\frac{J^{'}}{1}$ is

1

\frac{8}{3} π^{2}

2

\frac{3}{8 π^{2}}

3

\frac{3}{2} π^{2}

4

\frac{2}{3} π^{2}

Explanation:

b
$\begin{aligned} I_{md} = \frac{m ℓ^{2}}{3} \\ 2 π r = ℓ \\ r = \frac{ℓ}{2 π} \\ I^{'} = I_{Img} = \frac{1}{2} {mR}^{2} = \frac{m}{2} (\frac{ℓ^{2}}{4 π^{2}}) I^{'} = \frac{3}{8 π^{2}} \end{aligned}$

**NCERT-XI-I-116**

TEST SERIES (PHYSICS FST)

266229 Two particle of masses $m$ and 9 m are placed at a distance r . The gravitational potential at a point on the line joining them where the gravitational field is zero is:

1 Zero

2

- \frac{9 G m}{r}

3

\frac{16 Gm}{r}

4

- \frac{6 Gm}{r}

Explanation:

c
$\begin{aligned} \frac{G m}{x^{2}} = \frac{G (9 m)}{(r - x)^{2}} \\ \frac{1}{x} = \frac{3}{r - x} \Rightarrow r - x = 3 x \\ 4 x = r \Rightarrow x = \frac{r}{4} \end{aligned}$
The gravitational potential $= - \frac{Gm}{r / 4} - \frac{G (9 m)}{3 r / 4}$
$= - \frac{16 Gm}{Γ}$

**NCERT-XI-I-135**

TEST SERIES (PHYSICS FST)

266226 The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant $k$ and compresses it by length $L$ . The maximum velocity of the block after collision is:

1 Zero

2

\sqrt{\frac{2 k}{m}} L

3

\sqrt{\frac{k}{m}} L

4

\sqrt{M MLL}

Explanation:

c
When block of mass $M$ collides with the spring its kinetic energy gets converted into elastic potential energy of the spring
From the law of conservation of energy
$\frac{1}{2} M v^{2} = \frac{1}{2} K L^{2} \Rightarrow v = \sqrt{\frac{K}{M}}$

**NCERT-XI-I-81**

TEST SERIES (PHYSICS FST)

266227 Assertion: The temperature at which Centigrade and Fahrenheit thermometers read the same is $- 60^{\circ}$ . Reas on: There is no relation between Fahrenheit and Centigrade temperature.

1 Both assertion and reason are true and the reason is the correct explanation of the assertion

2 Both assertion and reason are true but reason is not the correct explanation of the assertion

3 Assertion is true but reason is false

4 Assertion and reason both are false

Explanation:

d
The relation between F and Cscale is, $\frac{C}{5} = \frac{F - 32}{9}$ . If $F = C \Rightarrow C = - 40^{\circ} C$ , i.e., at $- 40^{\circ}$ the Centigrade and Fahrenheit thermometers reads the same.

**NCERT-XI-II-203**

TEST SERIES (PHYSICS FST)

266228 The moment of inertia of $a$ thin uniform rod rotating about the perpendicular axis passing through one end is $I$ . The same rod is bent into a ring and its moment of inertia about the diameter is $I^{'}$ , then the ratio $\frac{J^{'}}{1}$ is

1

\frac{8}{3} π^{2}

2

\frac{3}{8 π^{2}}

3

\frac{3}{2} π^{2}

4

\frac{2}{3} π^{2}

Explanation:

b
$\begin{aligned} I_{md} = \frac{m ℓ^{2}}{3} \\ 2 π r = ℓ \\ r = \frac{ℓ}{2 π} \\ I^{'} = I_{Img} = \frac{1}{2} {mR}^{2} = \frac{m}{2} (\frac{ℓ^{2}}{4 π^{2}}) I^{'} = \frac{3}{8 π^{2}} \end{aligned}$

**NCERT-XI-I-116**

TEST SERIES (PHYSICS FST)

266229 Two particle of masses $m$ and 9 m are placed at a distance r . The gravitational potential at a point on the line joining them where the gravitational field is zero is:

1 Zero

2

- \frac{9 G m}{r}

3

\frac{16 Gm}{r}

4

- \frac{6 Gm}{r}

Explanation:

c
$\begin{aligned} \frac{G m}{x^{2}} = \frac{G (9 m)}{(r - x)^{2}} \\ \frac{1}{x} = \frac{3}{r - x} \Rightarrow r - x = 3 x \\ 4 x = r \Rightarrow x = \frac{r}{4} \end{aligned}$
The gravitational potential $= - \frac{Gm}{r / 4} - \frac{G (9 m)}{3 r / 4}$
$= - \frac{16 Gm}{Γ}$

**NCERT-XI-I-135**

TEST SERIES (PHYSICS FST)

266226 The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant $k$ and compresses it by length $L$ . The maximum velocity of the block after collision is:

1 Zero

2

\sqrt{\frac{2 k}{m}} L

3

\sqrt{\frac{k}{m}} L

4

\sqrt{M MLL}

Explanation:

c
When block of mass $M$ collides with the spring its kinetic energy gets converted into elastic potential energy of the spring
From the law of conservation of energy
$\frac{1}{2} M v^{2} = \frac{1}{2} K L^{2} \Rightarrow v = \sqrt{\frac{K}{M}}$

**NCERT-XI-I-81**

TEST SERIES (PHYSICS FST)

266227 Assertion: The temperature at which Centigrade and Fahrenheit thermometers read the same is $- 60^{\circ}$ . Reas on: There is no relation between Fahrenheit and Centigrade temperature.

1 Both assertion and reason are true and the reason is the correct explanation of the assertion

2 Both assertion and reason are true but reason is not the correct explanation of the assertion

3 Assertion is true but reason is false

4 Assertion and reason both are false

Explanation:

d
The relation between F and Cscale is, $\frac{C}{5} = \frac{F - 32}{9}$ . If $F = C \Rightarrow C = - 40^{\circ} C$ , i.e., at $- 40^{\circ}$ the Centigrade and Fahrenheit thermometers reads the same.

**NCERT-XI-II-203**

TEST SERIES (PHYSICS FST)

266228 The moment of inertia of $a$ thin uniform rod rotating about the perpendicular axis passing through one end is $I$ . The same rod is bent into a ring and its moment of inertia about the diameter is $I^{'}$ , then the ratio $\frac{J^{'}}{1}$ is

1

\frac{8}{3} π^{2}

2

\frac{3}{8 π^{2}}

3

\frac{3}{2} π^{2}

4

\frac{2}{3} π^{2}

Explanation:

b
$\begin{aligned} I_{md} = \frac{m ℓ^{2}}{3} \\ 2 π r = ℓ \\ r = \frac{ℓ}{2 π} \\ I^{'} = I_{Img} = \frac{1}{2} {mR}^{2} = \frac{m}{2} (\frac{ℓ^{2}}{4 π^{2}}) I^{'} = \frac{3}{8 π^{2}} \end{aligned}$

**NCERT-XI-I-116**

TEST SERIES (PHYSICS FST)

266229 Two particle of masses $m$ and 9 m are placed at a distance r . The gravitational potential at a point on the line joining them where the gravitational field is zero is:

1 Zero

2

- \frac{9 G m}{r}

3

\frac{16 Gm}{r}

4

- \frac{6 Gm}{r}

Explanation:

c
$\begin{aligned} \frac{G m}{x^{2}} = \frac{G (9 m)}{(r - x)^{2}} \\ \frac{1}{x} = \frac{3}{r - x} \Rightarrow r - x = 3 x \\ 4 x = r \Rightarrow x = \frac{r}{4} \end{aligned}$
The gravitational potential $= - \frac{Gm}{r / 4} - \frac{G (9 m)}{3 r / 4}$
$= - \frac{16 Gm}{Γ}$

**NCERT-XI-I-135**

TEST SERIES (PHYSICS FST)

266226 The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant $k$ and compresses it by length $L$ . The maximum velocity of the block after collision is:

1 Zero

2

\sqrt{\frac{2 k}{m}} L

3

\sqrt{\frac{k}{m}} L

4

\sqrt{M MLL}

Explanation:

c
When block of mass $M$ collides with the spring its kinetic energy gets converted into elastic potential energy of the spring
From the law of conservation of energy
$\frac{1}{2} M v^{2} = \frac{1}{2} K L^{2} \Rightarrow v = \sqrt{\frac{K}{M}}$

**NCERT-XI-I-81**

TEST SERIES (PHYSICS FST)

266227 Assertion: The temperature at which Centigrade and Fahrenheit thermometers read the same is $- 60^{\circ}$ . Reas on: There is no relation between Fahrenheit and Centigrade temperature.

1 Both assertion and reason are true and the reason is the correct explanation of the assertion

2 Both assertion and reason are true but reason is not the correct explanation of the assertion

3 Assertion is true but reason is false

4 Assertion and reason both are false

Explanation:

d
The relation between F and Cscale is, $\frac{C}{5} = \frac{F - 32}{9}$ . If $F = C \Rightarrow C = - 40^{\circ} C$ , i.e., at $- 40^{\circ}$ the Centigrade and Fahrenheit thermometers reads the same.

**NCERT-XI-II-203**

TEST SERIES (PHYSICS FST)

266228 The moment of inertia of $a$ thin uniform rod rotating about the perpendicular axis passing through one end is $I$ . The same rod is bent into a ring and its moment of inertia about the diameter is $I^{'}$ , then the ratio $\frac{J^{'}}{1}$ is

1

\frac{8}{3} π^{2}

2

\frac{3}{8 π^{2}}

3

\frac{3}{2} π^{2}

4

\frac{2}{3} π^{2}

Explanation:

b
$\begin{aligned} I_{md} = \frac{m ℓ^{2}}{3} \\ 2 π r = ℓ \\ r = \frac{ℓ}{2 π} \\ I^{'} = I_{Img} = \frac{1}{2} {mR}^{2} = \frac{m}{2} (\frac{ℓ^{2}}{4 π^{2}}) I^{'} = \frac{3}{8 π^{2}} \end{aligned}$

**NCERT-XI-I-116**

TEST SERIES (PHYSICS FST)

266229 Two particle of masses $m$ and 9 m are placed at a distance r . The gravitational potential at a point on the line joining them where the gravitational field is zero is:

1 Zero

2

- \frac{9 G m}{r}

3

\frac{16 Gm}{r}

4

- \frac{6 Gm}{r}

Explanation:

c
$\begin{aligned} \frac{G m}{x^{2}} = \frac{G (9 m)}{(r - x)^{2}} \\ \frac{1}{x} = \frac{3}{r - x} \Rightarrow r - x = 3 x \\ 4 x = r \Rightarrow x = \frac{r}{4} \end{aligned}$
The gravitational potential $= - \frac{Gm}{r / 4} - \frac{G (9 m)}{3 r / 4}$
$= - \frac{16 Gm}{Γ}$

**NCERT-XI-I-135**

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