Question

Two rubber bands stretched to the standard length cause an object to accelerate at $2m/s^2$. Suppose another object with twice the mass is pulled by four rubber bands stretched to the standard length. What is the acceleration of the second object?

• A. $3m/s^2$
• B. $5m/s^2$
• C. $2m/s^2$
• D. $7m/s^2$

Answer 1

The correct option is C $2m/s^2$

The force is double and mass too is double,so cancels each other,and acceleration remain unchanged.

Let the force applied by two rubber bands is k Newton, mass of object be m kg.

$F1=m1a1$

$a1=F1/m1$

$a1=k/m$ ..........$eq1$

Now, the force applied by four rubber bands would be $2k$ Newton.

Here mass too is twice i.e. $2mkg.$

$F2=m2a2$

$a2=F2/m2$

$a2=2k/2m=x/m$ .... $eq2$

$a1=a2$

from both equation we get that in both the

condition acceleration is same.

so in the condition of $2$ rubber band the

acceleration is $2m/s²$

then for the condition of four rubber band and

twice the mass,the acceleration must be $2m/s².$

Hence,

option $C$ is correct answer.