Question

Two blocks of masses 2kg and 4 kg are hanging with the help of massless string passing over an ideal pulley inside an elevator. The elevator is moving upward with an acceleration of g/2.the tension in the string connected between the two blocks will be.

Answer 1

Step 1: Given that:

Mass($m_1$) of the first block = $2kg$

mass($m_2$) of the second block = $4kg$

The acceleration of the elevator in an upward direction = $\frac{g}{2}$

Step 2: Formula and concept used:

According to Newton's law of motion,

The net force on a body = Mass $\times$ Acceleration in the body

When a body is in rest in a accelerating frame of reference with respect to an observer in the same frame of reference, then the motion of the body is entirely described by using the concept of pseudo force.

Pseudo force on a body = The mass of the body $\times$ The accelerating of the observer(in opposite direction)

Acceleration due to gravity(g) = $10m{s}^{-2}$

Step 3: Calculation of the pseudo force on the blocks in the elevator:

The pseudo force on the block of mass 2kg for an observer in the elevator is given as;

= Mass of the block $\times$ Acceleration of the observer in the elevator

= $2\times \frac{g}{2}$

The pseudo force on the block of mass 4kg for an observer in the elevator is given as;

= $4kg\times \frac{g}{2}$

= $4\times \frac{g}{2}$

Step 4: Calculation of the tension in the string connected between the two blocks:

Now, using Newton's second law of motion, the free body diagram of the first block;

If the acceleration in the blocks is $\text{a}$, then

For the block of mass of 4kg;

$(4kg\times g+4kg\times \frac{g}{2})-T=4kg\times a$

$4g+4\frac{g}{2}-T=4a$..............(1)

For the block of mass 2kg;

$T-2kg\times \frac{g}{2}-2kg\times g=2kg\times a$

$T-2\frac{g}{2}-2g=2a$

$2T-2g-4g=4a$

$2T-6g=4a$................(2)

From equations (1) and (2), we get

$4g+4\frac{g}{2}-T=2T-6g$

$\Rightarrow 2T-6g=4g+4\frac{g}{2}-T$

$\Rightarrow 4T-12g=8g+4g-2T$

$\Rightarrow 6T=24g$

$\Rightarrow T=4g$

$\Rightarrow T=4\times 10m{s}^{-2}$

$\Rightarrow T=40N$

Thus,

The tension in the string connected between the two blocks = $40N$