Question

Q-8) the tension in the string in the pulley system shown is
A)75N
B)80N
C)7.5N
D)30N

Q-9) In question 8, find net force on the pulley
A)zero
B)150N
C)160N
D)60N

(Assume pulley to be massless)

Answer 1

Given :

→ A pulley system of two masses (10kg and 6kg) has been provided.

To Find :

→ Tension force in the string.

→ Net force on the pulley.

Concept :

☞ First, we have to find out acceleration of the system after that we can calculate tension force in the string.

Diagram :

→ Please, see the attachment for better understanding.

Calculation :

↗ Acceleration of the system :

$\Rightarrow\bf\:F_{net}=ma\\ \\ \Rightarrow\sf\:10g-6g=(10+6)a\\ \\ \Rightarrow\sf\:4g=16a\\ \\ \Rightarrow\sf\:a=\dfrac{4g}{16}\\ \\ \Rightarrow\underline{\boxed{\bf{a=\dfrac{g}{4}\:ms^{-2}}}}$

↗ Tension force in the string :

$\dag\sf\:For\:block\:of\:mass\:10kg\\ \\ \dashrightarrow\sf\:10g-T=10a\\ \\ \dashrightarrow\sf\:10g-T=10\times \dfrac{g}{4}\\ \\ \dashrightarrow\sf\:T=10g-\dfrac{10g}{4}\\ \\ \dashrightarrow\sf\:T=\dfrac{40g-10g}{4}\\ \\ \dashrightarrow\sf\:T=\dfrac{300}{4}\\ \\ \dashrightarrow\underline{\boxed{\bf{\red{T=75N}}}}\:\orange{\bigstar}$

↗ Net force on the pulley :

$\longrightarrow\sf\:F_p=2T\\ \\ \longrightarrow\sf\:F_p=2(75)\\ \\ \longrightarrow\underline{\boxed{\bf{\purple{F_p=150N}}}}\:\gray{\bigstar}$

____________________________

⚾ Answer-8 → (A) 75N

⚾ Answer-9 → (B) 150N