
A block of mass m = 1kg is placed on a smooth surface and is connected with a spring of constant K = 100N/m and another end of spring is connected to a fixed wall as shown. The block is pulled by a distance A = 0.10 m from its natural length and released at t = 0
(A) The maximum speed is after $t=\dfrac{\pi }{20}s$
(B) Time taken to cover the first 0.10 m, $t=\dfrac{\pi }{20}s$
(C) Time taken to cover the first 0.05 m, $t=\dfrac{\pi }{40}s$
(D) Time taken to cover the first 0.05 m, $t=\dfrac{\pi }{30}s$
Answer
568.8k+ views
Hint: In the question, a smooth floor is given which means that there is no friction in between the block and the floor, so, no amount of energy will be lost due to friction. Also, this case is a case of simple harmonic motion of a spring, which means it will oscillate at a specific frequency for a particular time period.
Formula used:
For solving this question, we will be using the formula for angular frequency of a spring in simple harmonic motion, i.e.,
$\omega =\sqrt{\dfrac{K}{m}}$
And, the formula
$T=\dfrac{2\pi }{\omega }$
Complete answer:
First, let us take a look at the given parameters,
K = 100N/m
m = 1 kg
L = 1 m
Now, using the formula for the angular frequency of a spring in simple harmonic motion,
$\omega =\sqrt{\dfrac{K}{m}}$
Using the given parameters
$\Rightarrow \omega =\sqrt{\dfrac{100}{1}}$
$\Rightarrow \omega =10rad/s$
Now that we have the angular acceleration,
So, using
$T=\dfrac{2\pi }{\omega }$
Now, the maximum speed of the spring will be at its natural length,
So,
$\Rightarrow \dfrac{T}{4}=\dfrac{2\pi }{10\times 4}$
$\Rightarrow \dfrac{T}{4}=\dfrac{\pi }{20}s$
Now, the time taken to cover 0.1m is $\dfrac{T}{4}=\dfrac{\pi }{20}s$
Now, Time taken to cover 0.05 m will be
$\Rightarrow \dfrac{T}{4}\times \dfrac{2}{3}$
$\Rightarrow \dfrac{\pi }{20}\times \dfrac{2}{3}$
$\Rightarrow \dfrac{\pi }{30}s$
So, the correct options will be,
Option (A) The maximum speed is after $t=\dfrac{\pi }{20}s$ , Option (B) Time taken to cover the first 0.10 m, $t=\dfrac{\pi }{20}s$ and Option (D) Time taken to cover the first 0.05 m, $t=\dfrac{\pi }{30}s$
Note:
Simple harmonic motion is a special form of periodic motion in dynamics and physics where the restoring force on the moving object is directly proportional to the displacement magnitude of the object and works against the equilibrium position of the object.
Formula used:
For solving this question, we will be using the formula for angular frequency of a spring in simple harmonic motion, i.e.,
$\omega =\sqrt{\dfrac{K}{m}}$
And, the formula
$T=\dfrac{2\pi }{\omega }$
Complete answer:
First, let us take a look at the given parameters,
K = 100N/m
m = 1 kg
L = 1 m
Now, using the formula for the angular frequency of a spring in simple harmonic motion,
$\omega =\sqrt{\dfrac{K}{m}}$
Using the given parameters
$\Rightarrow \omega =\sqrt{\dfrac{100}{1}}$
$\Rightarrow \omega =10rad/s$
Now that we have the angular acceleration,
So, using
$T=\dfrac{2\pi }{\omega }$
Now, the maximum speed of the spring will be at its natural length,
So,
$\Rightarrow \dfrac{T}{4}=\dfrac{2\pi }{10\times 4}$
$\Rightarrow \dfrac{T}{4}=\dfrac{\pi }{20}s$
Now, the time taken to cover 0.1m is $\dfrac{T}{4}=\dfrac{\pi }{20}s$
Now, Time taken to cover 0.05 m will be
$\Rightarrow \dfrac{T}{4}\times \dfrac{2}{3}$
$\Rightarrow \dfrac{\pi }{20}\times \dfrac{2}{3}$
$\Rightarrow \dfrac{\pi }{30}s$
So, the correct options will be,
Option (A) The maximum speed is after $t=\dfrac{\pi }{20}s$ , Option (B) Time taken to cover the first 0.10 m, $t=\dfrac{\pi }{20}s$ and Option (D) Time taken to cover the first 0.05 m, $t=\dfrac{\pi }{30}s$
Note:
Simple harmonic motion is a special form of periodic motion in dynamics and physics where the restoring force on the moving object is directly proportional to the displacement magnitude of the object and works against the equilibrium position of the object.
Recently Updated Pages
A man running at a speed 5 ms is viewed in the side class 12 physics CBSE

The number of solutions in x in 02pi for which sqrt class 12 maths CBSE

State and explain Hardy Weinbergs Principle class 12 biology CBSE

Write any two methods of preparation of phenol Give class 12 chemistry CBSE

Which of the following statements is wrong a Amnion class 12 biology CBSE

Differentiate between action potential and resting class 12 biology CBSE

Trending doubts
What are the major means of transport Explain each class 12 social science CBSE

Which are the Top 10 Largest Countries of the World?

Draw a labelled sketch of the human eye class 12 physics CBSE

How much time does it take to bleed after eating p class 12 biology CBSE

Explain sex determination in humans with line diag class 12 biology CBSE

Explain sex determination in humans with the help of class 12 biology CBSE

