Spring-block system in an accelerated car

Classical Mechanics Level 3

A block of mass $m$ is suspended by an ideal spring of force constant $k$ from the ceiling of a car. The car is traveling at a constant speed along a circular path with a net acceleration $a$ .

Due to the acceleration of the car the block and the spring system tilts by an angle $\theta$ with the vertical. In this position, the block is displaced slightly along the spring and released. What will be the time period of the small oscillations of the block?

2 \pi \sqrt{\dfrac{m}{k}}

2\pi \sqrt{\dfrac{m\sqrt{a^2+g^2}}{kg}}

2\pi \sqrt{\dfrac{mg+ma}{kg}}

2\pi \sqrt{\dfrac{mg}{k \sqrt{a^2+g^2}}}

2 solutions

Md Zuhair
May 11, 2017

Very funny to see that all the other options are dimensionally wrong ...

Well That was a shortcut, But here , we can see that

$mg \cos \theta = k x \cos \theta$

$\implies mg = kx$

$\implies \dfrac{g}{x} = \dfrac{m}{k}$

And we know $T= 2 \pi \sqrt{\dfrac{a}{x}}$ $\implies T= 2 \pi \sqrt{\dfrac{g}{x}} \implies T= 2 \pi \sqrt{\dfrac{m}{k}}$

Great solution!!!!

A Former Brilliant Member - 4 years, 1 month ago

Well, Thank you

Md Zuhair - 4 years ago

Can u give me a diagram if u don't mind , sir

Aman Bhandare - 4 years ago

@Aman Bhandare – Hey. NO sir. I am a school boy. Yeah I will add it when I open my computer

Md Zuhair - 4 years ago

@Md Zuhair – No no Zuhair is a great sir...aren't u Zuhair?😜😜

rajdeep brahma - 3 years, 4 months ago

@Rajdeep Brahma – Chatuni :P... Amra toh eki dole chilam :P. Dol bodol :P. Naki single single :P

Md Zuhair - 3 years, 4 months ago

@Md Zuhair – na na same team vs dipu aunty. :)

rajdeep brahma - 3 years, 2 months ago

@Rajdeep Brahma – HAHA! Nischoi.. @Dipanwita Guhathakurta . Dekho..

Md Zuhair - 3 years, 2 months ago

How is T=2π√a/x

Sangita Saxena - 2 years, 11 months ago

how are they dimensionally incorrect?

Rohan Joshi - 4 months, 4 weeks ago

it was when they created the question and i solved it, now they are edited actually

Md Zuhair - 3 months, 2 weeks ago

A Former Brilliant Member
May 11, 2017

Please change the options ,it becomes horribly easy with the given ones.

Type it in the reports

Md Zuhair - 4 years ago

I have reported the question.

A Former Brilliant Member - 4 years ago

It seems overrated too

Md Zuhair - 4 years ago

@Md Zuhair – Exactly. Not more than a level 2 question.

A Former Brilliant Member - 4 years ago

Spring-block system in an accelerated car

2 solutions

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