Question

Challenge for Physics Lovers !
Question : In the system shown in the figure, the acceleration of 1kg mass is
A) g/4 downwards
B) g/2 downwards
C) g/2 upwards
D) g/4 upwards

Class : 11th/Physics/NLM​

Answer 1

Given :

▪ Mass of block A = 4kg

▪ Mass of block B = 1kg

To Find :

▪ Acceleration of 1kg mass.

Diagram :

↗ Please, see the attachment for better understanding.

Calculation :

☞ If a is downward acceleration of block A (4kg), the upward acceleration of block B (1kg) must be 2a.

☞ Let T be tension in each part of string.

☞ The equation of motion on 4kg block is

$\dashrightarrow\sf\:4g-2T=4a\rightarrow\:(1)$

☞ The equation of motion on 1kg block is

$\dashrightarrow\sf\:T-1g=1\times 2a\\ \\ \rightarrow\sf\:2T-2g=4a\rightarrow\:(2)$

✴ Adding (1) and (2), we get

$\dashrightarrow\sf\:2g=8a\\ \\ \dashrightarrow\sf\:a=\dfrac{g}{4}\\ \\ \therefore\bf\:Acc.\:of\:block\:B=2a=\dfrac{g}{2}\:upwards$

Option-C is correct ✔

Be Brainly ☺

Answer 2

Let ,

Mass of block A = 1 kg

Mass of block B = 4 kg

We need to find the acceleration of 1 kg mass.

For 4 kg block :

⇒ mg - Tnet = ma

⇒ 4g - 2T = 4a ... (1)

For 1 kg block :

⇒ T - 1g = 2a

⇒ T - g = 2a

⇒ 2T - 2g = 4a ...  (2)

Now solve , (1) + (2) ,

⇒ 2g = 8a

⇒ a = g/4

So , acceleration of 1 kg block is 2a = g/2 upwards