- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Two objects of masses $m_1$ and $m_2$ having the same size are dropped simultaneously from heights $h_1$ and $h_2$ respectively. Find out the ratio of time they would take in reaching the ground. Will this ratio remain the same if

$(i)$ one of the objects is hollow and the other one is solid and

$(ii)$ both of them are hollow, size remaining the same in each case. Give reason.

As given, two objects of masses $m_1$ and $m_2$ having the same size are dropped simultaneously from heights $h_1$ and $h_2$ respectively.

**Here for mass $m_1$:**

Initial velocity $u=0$

Acceleration $a=g$

Distance $s=h_1$

Let the time taken is $t_1$

On using second equation of motion, $h=ut+\frac{1}{2}gt^2$

Or $h_1=0+\frac{1}{2}gt_1^2$

Or $h_1=\frac{1}{2}gt_1^2$

Or $t_1=\sqrt{\frac{2h_1}{g}}$

Similarly, for an object having mass $m_2$, let $t_2$ is taken to reach the ground.

So, $t_2=\sqrt{\frac{2h_2}{g}}$

Now, $\frac{t_1}{t_2}=\frac{\sqrt{\frac{2h_1}{g}}}{\sqrt{\frac{2h_2}{g}}}$

Or $\frac{t_1}{t_2}=\sqrt{\frac{h_1}{h_2}}$

So, the ratio of time will remain the same if $(i)$ one of the objects is hollow and the other one is solid and $(ii)$ both of them are hollow, the size remaining the same in each case.

- Related Questions & Answers
- Sum of the series 1 / 1 + (1 + 2) / (1 * 2) + (1 + 2 + 3) / (1 * 2 * 3) + … + upto n terms in C++
- Sum of the series 1 + (1+2) + (1+2+3) + (1+2+3+4) + ... + (1+2+3+4+...+n) in C++
- C++ program to find the sum of the series 1 + 1/2^2 + 1/3^3 + …..+ 1/n^n
- Sum of series 1^2 + 3^2 + 5^2 + . . . + (2*n – 1)^2
- Sum of series 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2 in C++
- Sum of the Series 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + ... in C++
- Sum of the series 2^0 + 2^1 + 2^2 +...+ 2^n in C++
- Count the number of ways to tile the floor of size n x m using 1 x m size tiles in C++
- Calculate the value of (m)1/n in JavaScript
- Sum of the series Kn + ( K(n-1) * (K-1)1 ) + ( K(n-2) * (K-1)2 ) + ... (K-1)n in C++
- Find Sum of Series 1^2 - 2^2 + 3^2 - 4^2 ... upto n terms in C++
- Find the Number of subarrays having sum of the form k^m, m >= 0 using C++
- Largest number with binary representation is m 1’s and m-1 0’s in C++
- Sum of the series 1^1 + 2^2 + 3^3 + ... + n^n using recursion in C++
- Program to find sum of series 1 + 1/2 + 1/3 + 1/4 + .. + 1/n in C++
- C++ program to find the sum of the series 1/1! + 2/2! + 3/3! + 4/4! +…….+ n/n!