Question

Two blocks of mass m = 5 kg and M = 10 kg are connected by a string passing
over a pulley B as shown. Another string connects the centre of pulley B to the
noor and passes over another pulley A as shown. An upward force F is applied
at the centre of pulley A. Both the pulleys are massless.
Find the acceleration of blocks m and M if Fis:
(a) 100 N
(b) 300 N
(C) 500 N (take g = 10 m/s)
(
в
mN​

Answer 1

Answer:

Explanation:For Few=300N

T=F/4=75 Tmg, M will be remain stationary on the floor,whereas m will move.So Acceleration of m, a=(T-mg)/m=(75-50)/5 = 5m/s2.

Answer 2

Answer:

(a). If the force is 100 N then the blocks do not accelerate.

(b). If the force is 300 N then the block m will accelerate with 5 m/s².

(c). If the force is 500 N then both the block  will be accelerate with 15 m/s² and  2.5 m/s².

Explanation:

Let the tension in the string passing over A is T₀.

The tension in the string passing over B is T.

According to FBD,

$F=2T_{0}$

$T_{0}=2T$

So, $T=\dfrac{F}{4}$

(a). If force is 100 N

We need to calculate the weight of the both block

Weight of the block m = 50 N

Weight of the block M= 100 N

We need to calculate the tension

Using formula of tension

$T=\dfrac{F}{4}$

Put the value of F

$T=\dfrac{100}{4}=25\ N$

Here, T<mg and T<Mg

So, both the block remain stationary on the floor

(b). If the force is 300 N

We need to calculate the tension

Using formula of tension

$T=\dfrac{F}{4}$

Put the value of F

$T=\dfrac{300}{4}=75\ N$

Here, T>mg and T<Mg

So, block M will remain stationary on the floor and block m will move

We need to calculate the acceleration

Using formula of acceleration

$a=\dfrac{T-mg}{m}$

$a=\dfrac{75-50}{5}$

$a=5\ m/s^2$

(c). If the force is 500 N

We need to calculate the tension

$T=\dfrac{500}{4}=125\ N$

Here, T>mg and T>Mg

So, both the block will accelerate upward

We need to calculate the acceleration of m block

$a=\dfrac{T-mg}{m}$

$a=\dfrac{125-50}{5}$

$a=15\ m/s^2$

We need to calculate the acceleration of M block

$a=\dfrac{125-100}{10}$

$a=2.5\ m/s^2$

Hence, (a). If the force is 100 N then the blocks do not accelerate.

(b). If the force is 300 N then the block m will accelerate with 5 m/s².

(c). If the force is 500 N then both the block  will be accelerate with 15 m/s² and  2.5 m/s².