Tag: physics

Questions Related to physics

A sphere $A$ moving with speed $u$ and rotating with an angular velocity $\omega$ makes a head-on elastic collision with an identical stationary sphere $B$. There is no friction between the surfaces of $A$ and $B$. Choose the correct alternative(s). Discard gravity.

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. $A$ will stop moving but continue to rotate with an angular velocity $\omega$

  2. $A$ will come to rest and stop rotating

  3. $B$ will move with speed $u$ without rotating

  4. $B$ will move with speed $u$ and rotate with an angular velocity $\omega$.

Show answer
Correct Option: A,C
Explanation:
Let $m$ be the mass of sphere and $v _1$ and $v _2$ be the velocities of the spheres A and B respectively after the collision.
Applying conservation of linear momentum:        $P _i = P _f$
$m  u + 0 = mv _1  + mv _2           \implies v _1 + v _2 = u$      ........(1)
Also $\dfrac{v _2- v _1}{ u-0} = -1         \implies v _1 - v _2 = -u$  
On solving we get,       $v _1 = 0 $   and $v _2 = u$
Thus A will stop and B will move with $u$
Also as there is no friction between the A and B, thus there will be no torque. Hence angular velocities of the respective spheres must remains the same as it was initially.
So, A will continue to rotate with $w$ whereas B will not rotate.

A 20 g ball is fired horizontally toward a 100 g ball that is hanging motionless from a 1.0-m-long string. The balls undergo a head-on, elastic collision, after which the 100 g ball swings out to a maximum angle of 50 degrees. Determine the initial speed of the 20 g ball.

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. 8.4m/s

  2. 4.2m/s

  3. 2.1m/s

  4. 16.8m/s

Show answer
Correct Option: A
Explanation:

At first we can find the final velocity of the $100\ g$ ball.

$ \dfrac { { m } _{ 2 }{ { v } _{ 2 } }^{ 2 } }{ 2 } =mgh={ m } _{ 2 }gl(1-cos\alpha )$

$ \implies { v } _{ 2 }=\sqrt { 2gl\left( 1-cos\alpha  \right)  } =\sqrt { 2*9.81*1.1(1-cos{ 50 }^{ o }) } =2.78m/s $

Now applying conservation of the momentum principle, we get:

$ { m } _{ 1 }{ V } _{ 1 }+{ m } _{ 2 }{ V } _{ 2 }={ m } _{ 1 }{ v } _{ 1 }+{ m } _{ 2 }{ v } _{ 2 }$

$ { v } _{ 1 }=\dfrac { { m } _{ 1 }{ V } _{ 1 }-{ m } _{ 2 }{ v } _{ 2 } }{ { m } _{ 1 } } ={ V } _{ 1 }-{ v } _{ 2 }\dfrac { { m } _{ 2 } }{ { m } _{ 1 } } $

Principle of kinetic energy conservation , we get 

$ \dfrac { 1 }{ 2 } { m } _{ 1 }{ { { V } _{ 1 } }^{ 2 } }+\dfrac { 1 }{ 2 } { m } _{ 2 }{ { V } _{ 2 } }^{ 2 }=\dfrac { 1 }{ 2 } { m } _{ 1 }{ { v } _{ 1 } }^{ 2 }+\dfrac { 1 }{ 2 } { m } _{ 2 }{ { v } _{ 2 } }^{ 2 }$


$ { v } _{ 1 }={ V } _{ 1 }-{ v } _{ 2 }\dfrac { { m } _{ 2 } }{ { m } _{ 1 } } \ { V } _{ 2 }=0$

$\implies { V } _{ 1 }=\dfrac { { { { { m } _{ 1 } }^{ 2 }v } _{ 1 } }^{ 2 }+{ m } _{ 2 }{ m } _{ 1 }{ { v } _{ 2 } }^{ 2 } }{ 2{ m } _{ 1 }{ v } _{ 2 }{ m } _{ 2 } } =\dfrac { v _{ 2 }\left( { m } _{ 2 }+{ m } _{ 1 } \right)  }{ 2{ m } _{ 1 } } $

$ \implies  \dfrac { 2.78\left( 0.1+0.024 \right)  }{ 2*0.024 } =8.4m/s$

Which of the following is logically equivalent to $(p\wedge q)$ ?

physics electronic devices boolean algebra digital electronics and logic gates logic gates

  1. $p\rightarrow q$

  2. $\sim p \, \wedge \sim q$

  3. $p\, \wedge \sim q$

  4. $\sim (p\rightarrow \sim q)$

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Correct Option: D

The Boolean expression $P+\overline { P } Q$, where $P$ and $Q$ are the inputs of the logic circuit, represents  

physics electronic devices boolean algebra digital electronics and logic gates logic gates

  1. AND gate

  2. NAND gate

  3. NOT gate

  4. OR gate

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Correct Option: A

Person who use boolean algebra for describing the operation of logic gates first was

physics electronic devices boolean algebra digital electronics and logic gates logic gates

  1. Boole

  2. Shannon

  3. Schottky

  4. Zener

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Correct Option: B
Explanation:

Person who use boolean algebra for describing the operation of logic gates first was Claude Shannon. 

In the binary number system, the number $100$ represents

physics electronic devices boolean algebra digital electronics and logic gates logic gates

  1. one

  2. three

  3. four

  4. hundred

Show answer
Correct Option: C
Explanation:

In binary number system only $0$'s and $1$'s are used to built the whole number system.
Hence,
$0 = 0$
$1 = 1$
Start back at $0$ again, but add $1$ on the left,
$2 = 10$
$3 = 11$
Start back at $0$ again, and add one to the number on the left, but that number is already at $1$, so it also goes back to $0$ and $1$ is added to the next position on the left. Hence,
$4 = 100$ .... and so on.

Boolean algebra is essentially based on 

physics electronic devices boolean algebra digital electronics and logic gates logic gates

  1. symbols

  2. logic

  3. truth

  4. numbers

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Correct Option: B
Explanation:

Boolean algebra is essentially based on logic. It is also known as logical algebra.

The Boolean algebra uses

physics electronic devices boolean algebra digital electronics and logic gates logic gates

  1. two digits, $0$ and $1$.

  2. two digits, $1$ and $2$.

  3. two digits, $0$ and $2$.

  4. $10$ digits, $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$.

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Correct Option: A
Explanation:

The Boolean algebra uses binary number system i.e. two digits $0$ and $1$.

The value of $\bar{1}$ +$\bar{1}$  is

physics electronic devices boolean algebra digital electronics and logic gates logic gates

  1. $2$

  2. $0$

  3. $1$

  4. $10$

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Correct Option: B
Explanation:

$\bar 1 + \bar 1 = 0 + 0 = 0$

What is the value of $A + \bar{A}$ in the Boolean algebra?

physics electronic devices boolean algebra digital electronics and logic gates logic gates

  1. $0$

  2. $A$

  3. $1$

  4. $\bar{A}$

Show answer
Correct Option: C
Explanation:

When $A = 1,$ then $A + \bar{A} = 1 + 0 =1$
and when $A = 0$, then $A + \bar{A} = 0 + 1 = 1$