Question

Block A is moving with acceleration A along a frictionless horizontal surface. When a second block, B is placed on top of Block A the acceleration of the combined blocks drops to 1/5 the original value. What is the ratio of the mass of A to the mass of B?(a) 5 : 1 (b) 1 : 4(c) 3 : 1 (d) 2 : 1

Answer 1

the answer is a. 5:1
I hope this answer is correct

Answer 2

Answer:

The ratio of the mass of A to the mass of B is 1:4.

Explanation:

let us consider block A having mass m₁ and block B having mass m₂.

The force acting on block A is

$F= ma$....(I)

When a second block, B is placed on top of Block A the acceleration of the combined blocks drops to 1/5 the original value.

The force action on block B is

$F=(m_{1}+m_{2})\dfrac{a}{5}$.....(II)

From equation (I) and (II)

$m_{1}a=(m_{1}+m_{2})\dfrac{a}{5}$

$m_{1}-\dfrac{m_{1}}{5}=\dfrac{m_{2}}{5}$

$\dfrac{4m_{1}}{5}=\dfrac{m_{2}}{5}$

$\dfrac{m_{1}}{m_{2}}=\dfrac{1}{4}$

Hence, The ratio of the mass of A to the mass of B is 1:4.