Tag: physics

Questions Related to physics

At an airport, a bored child starts to walk backwards on a moving platform. The child accelerates relative to the platform with $a =  - 0.5m/{s^2}$ relative to the platform. The platform moves with a constant speed $v =  + 1.0m/s$ relative to the stationary floor. In $4.0$ seconds, how much will the child have been displaced relative to the floor?

physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

  1. $8m$

  2. $0m$

  3. $3m$

  4. $4m$

Show answer
Correct Option: B
Explanation:
initial vel = vel of platform $=1\ m/s$
acceleration wrt floor $=$ acceleration of him wrt platform +acc. of platform
$=\dfrac {-1}{2}m/s^2+0=\dfrac {-1}{2}m/s^2$
So, for finding displacement of him in us,
Applying second equation of motion
$x=ut +\dfrac {at^2}{2}$
$(1)(4)^2-\left (\dfrac {1}{4}\right) \dfrac {(4)^2}{2}$
$x=4-\dfrac {(4)^2}{4}=0\ m$

An open lift is moving upwards with velocity $10m/s$. It has an upward acceleration of $2m/{s^2}$. A ball is projected upwards with upwards with velocity $20m/s$ relative to the ground. Find the time when the ball again meets the lift.

physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

  1. $\frac{5}{3}s$

  2. $\frac{4}{3}s$

  3. $\frac{3}{4}s$

  4. $\frac{1}{4}s$

Show answer
Correct Option: A
Explanation:
Let the time of Height of the ball be $t$. Then. with respect to the lift.
$V _{B/L}= V _{B}-V _{L}= 20-10= 10\ m/s$
$a _{B/L}=a _{B}-a _{L}=(-10)-(2)=-12\ m/s^{2}$
To find $t$, applying second $eq^{n}$ to motion 
$h =u (t)+ at^{2}$
$\Rightarrow o= (10)(t)+ \dfrac{(-12)t^{2}}{2}$
$\Rightarrow bt^{2}=10 t$
$\Rightarrow t = 5/3^{3}$
Option $-A$ is correct. 

An elevator car whose floor-to-ceiling distance is equal to 2.7m starts ascending with a constant acceleration $1.2m/{s^2};2.0s$ after the start a bolt begins falling from the ceiling of the car. Find the displacement covered by the bolt during the free fall in the reference frame fixed to the elevator shaft.

physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

  1. 0.7 m

  2. 1.7 m

  3. 2.7 m

  4. 3.7 m

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Correct Option: A
Explanation:
Let the total time of free fall be $t$
Then at $t=2s$
$4 _{B}=2. \dfrac{1}{m}/s$          $4 _{C}=2.\dfrac{1}{m}/s$
$a _{C}=1.2\ m/s^{2}$              $a _{B}=-10\ m/s^{2}$
Wrt car.
distance travelled by bolt $= 27\ m$
Then 
$-2.7\ m=(4 _{B/C})t+a _{B/C}\left(\dfrac{t^{2}}{2}\right)$
$\Rightarrow -2.7= (2.4-2.4)t (\dfrac{-10-12}{2}) t^{2}$
$\Rightarrow 2.7= \dfrac{11.2}{2}t^{2}$
$\Rightarrow t^{2}=\left(\dfrac{2.7}{11.2}\times 2\right)^{-11}=0.482\ s^{2}$
Note: $4 _{B}=4 _{C}$ till $t=2.3$ before the both spots to fall. 
$4 _{B}=4 _{C}=a _{C}t=(1.2)(2)=2.4 m/s$
let the displacement of the bolt be $h$ Then, 
$h=4 _{B}(t)+4 _{\dfrac{B}{2}}t^{2}$
$h=(2.4)\sqrt{0.482}\dfrac{-(10)}{2}(0.482)$
$h=-0.743$
$h=\approx -0.7\ m$
$|h|\approx 0.7\ m$
Option $A$ is correct

A boy sitting on the top most berth in the compartment of a train which is just going to stop on the railway station, drops an apple aiming at the open hand of his brother situated vertically below his hands at a distance of about 2 m. The apple will fall

physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

  1. In the hand of his brother

  2. Slightly away from the hand of his brother in the direction of the motion of the train.

  3. Slightly away from the hands of his brother in the direction opposite to the direction of the motion of the train.

  4. None of these

Show answer
Correct Option: B
Explanation:

As both the boy and his brother are moving in same frame,and train is going to be slow down when the train will de-accelerate it will impart an inertia force in opposite direction but at the same time the boy will drop an apple from 2m height . when the train will exert inertia force on boy due to action reaction boy will also expert an force in forward direction due to which he will not able to put the apple in the hand of his brother and it will fall in forward direction.

The distance covered by a body moving alone-X-axis with initial velocity 'u' and uniform acceleration 'a' is given by $\displaystyle x=ut+\frac{1}{2}at^{2}$. This result is a consequence of

physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

  1. Newton's Ist law

  2. Newton's IInd law

  3. Newton IIIrd law

  4. None of the above

Show answer
Correct Option: D
Explanation:

There is no relation between NLM and given equation

A cart begins from rest at the top of a long incline and rolls with a constant acceleration of $2m/s^{2}$. How far has the cart moved along the incline after rolling for $3$ seconds?

physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

  1. $3$ meters

  2. $6$ meters

  3. $9$ meters

  4. $18$ meters

Show answer
Correct Option: C
Explanation:

Initial velocity of cart      $u =0  m/s$

Acceleration of the cart       $a = 2$ $m/s^2$
Distance covered by cart in 3 seconds       $S = ut + \dfrac{1}{2}at^2$                  where  $t =3$ seconds
$\therefore$    $S = 0 + \dfrac{1}{2 } \times 2 \times 3^2  = 9$  meters

A car was travelling at a speed of 10 m/s. After the brakes were applied, it start to decelerate at a rate of 2 $m/s^2$ and finally came to rest. Find the distance traveled by the car before coming to rest.

physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

  1. 10 m

  2. 15 m

  3. 25 m

  4. 35 m

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Correct Option: C
Explanation:
Initial speed of the car   $u = 10 \ m/s$
Final speed of the car   $v =  0 \ m/s$
Acceleration (or  retardation) of the car   $a = -2 \ m/s$
Using   $v^2 - u^2 = 2aS$
$\therefore$   $0 - 10^2 = 2(-2)S$
$\implies \ S = \dfrac{100}{2\times 2}  = 25 \ m$

The initial velocity of a particle (at $t = 0$) is $u$ and the acceleration by $f$ of particle at time $t$ is given $f=at$. Where $a$ is a constant which of the following relation for velocity $v$ of particle after time $t$ is turn 

physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

  1. $v\, =\, u\, +\, at^2$

  2. $v\, =\, u\, +\, \displaystyle \frac{at^2}{2}$

  3. $v\, =\, u\, +\, at$

  4. $v\, =\, u$

Show answer
Correct Option: C
Explanation:

We know that,

$\dfrac{dv}{dt} = a$
Hence,
$dv = a dt$
Integrating this and applying the proper limits.
$v  - u = at$
$\implies v=u+at$
Hence, option C is correct.

Identify the methods by which a magnet can be demagnetized.

physics properties of a magnetic field let's make a magnet making magnets making and handling magnets

  1. Heating a magnet strongly

  2. Repeated hammering of the magnet

  3. Storing it aligned with the N-S direction

  4. None of these

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Correct Option: A,B
Explanation:

Methods by which a magnet can be demagnetized can be given as mentioned below: 
$(1)$ Heating a magnet strongly
$(2)$ Hammering the magnet several times or repeated hammering
$(3)$ By passing an alternating current through the magnet
Hence, the correct options $(A)$ and $(B)$.

A permanent magnet can lose its magnetism with time 

physics fun with magnets let's make a magnet making magnets making and handling magnets

  1. True

  2. False

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Correct Option: A
Explanation:
Yes permanent magnet can lose its magnetism in following cases
i) Heating up to certain temperature
ii) Low coercivity and wrong storage.
iii)Energy transfer them by shock.