A force of $5 N$ produces an acceleration of $8 m s^{- 2}$ on a mass $m_{1}$ and an acceleration of $24 m s^{- 2}$ on a mass $m_{2}$ . What acceleration (in $m s^{- 2}$ ) would the same force provide if both the masses are tied together?

Open in App

Solution

Step1: Given data
A force of $5 N$ produces an acceleration of $8 m s^{- 2}$ on a mass $m_{1}$ and acceleration of $24 m s^{- 2}$ on a mass $m_{2}$ .
Step2: Formula used
$F = m \times a [w h e r e F = f o r c e, m = m a s s, a = a c c e l e r a t i o n]$
Step3: Calculating acceleration
Force is defined as the product of mass and acceleration. $F = m \times a$
Here, the force applied is the same on masses $m_{1} a n d m_{2}$
Mass will be obtained by dividing the force with the acceleration produced by the mass. $m = \frac{F}{a}$
Mass $m_{1}$ is obtained by dividing the force of $5 N$ with the acceleration of $8 m s^{- 2}$
$m_{1} = \frac{F}{a_{1}} m_{1} = \frac{5}{8} k g [a_{1} = 8 m s^{- 2}, F = 5 N]$
Mass $m_{2}$ is obtained by dividing the force of $5 N$ with the acceleration of $24 m s^{- 2}$
$m_{2} = \frac{F}{a_{2}} m_{2} = \frac{5}{24} k g [a_{2} = 24 m s^{- 2}, F = 5 N]$
The resultant mass when both the masses are tied together will be
$M = m_{1} + m_{2} M = \frac{5}{8} + \frac{5}{24} [m_{1} = \frac{5}{8} k g, m_{2} = \frac{5}{24} k g] M = \frac{20}{24} M = \frac{5}{6} k g$
The mass resulting when the two masses are combined is $\frac{5}{6} k g$ .
Acceleration (in $m s^{- 2}$ ) when both the masses are tied together is
$a = \frac{F}{m} a = \frac{5}{\frac{5}{6}} [F = 5 N, m = \frac{5}{6} k g] a = 6 m s^{- 2}$
Hence, the acceleration produced when the masses are tied together with the same force will be $6 m s^{- 2}$ .

Suggest Corrections

Similar questions

Q. A force of

5 N

produces an acceleration of 8

m s^{- 2}

on a mass

m_{1}

and an acceleration of 24

m s^{- 2}

on a mass

m_{2}

. What acceleration (in

m s^{- 2}

) would the same force provide if both the masses are tied together?

A force of 5 N produces an acceleration of 8 m $s^{- 2}$ on a mass $m_{1}$ and an acceleration of 24 m $s^{- 2}$ on mass $m_{2}$ . What acceleration would the same force provide if both the masses are tied together?

Q. Question 19
Derive the unit a force using the second law of motion. A force of 5 N produces an acceleration of

8 m s^{- 2}

on a mass

m_{1}

and an acceleration of

24 m s^{- 2}

on mass

m_{2}

. What acceleration would the same force provide if both the masses are tired together?

Q. 32.A force of 5N produces an acceleration of 8ms^-2 on a mass M1 and an acceleration of 24ms^-2 on a mass M2 what is acceleration in ms^-2would the same force provide of both the masses are tied ?

Q. A force of 5 N gives a mass m1, an acceleration of 10ms-2, and a mass m2, an acceleration of 20 ms-2.What acceleration would it give if both the bodies were tied together?

Join BYJU'S Learning Program

A force of 5N produces an acceleration of 8ms-2 on a mass m1 and an acceleration of 24ms-2 on a mass m2. What acceleration (in ms-2) would the same force provide if both the masses are tied together?

A force of $5 N$ produces an acceleration of $8 m s^{- 2}$ on a mass $m_{1}$ and an acceleration of $24 m s^{- 2}$ on a mass $m_{2}$ . What acceleration (in $m s^{- 2}$ ) would the same force provide if both the masses are tied together?