Question

A block of mass $3kg$ which is on a smooth inclined plane making an angle of ${30}^{\circ }$ to the horizontal is connected by second block of mass $2kg$ hanging vertically, What is the acceleration of each block and what is the tension of the cord?

• A. $0.98m/s^2;17.6N$
• B. $1.98m/s^2;19.6N$
• C. $0.49m/s^2;9.8N$
• D. $1.47m/s^2;4.9N$

Answer 1

The correct option is A $0.98m/s^2;17.6N$

Given,

Mass of block A, $m_a=3kg$

Mass of block B, $m_b=2kg$

Forces on $2kg$block

$m_{b}g-T=m_{b}a......\left(1\right)$

Forces on $3kg$ block

$T-m_{a}g\sin {30}^o=m_{a}a......\left(2\right)$

From (1) and (2)

$a=\frac{m_{b}g-m_{a}g\sin {30}^o}{m_a+m_b}=\frac{2\times 9.81-3\times 9.81\times 0.5}{2+3}=0.981m/s^2$

Put value of $a$ in equation (1)

$T=m_{b}g-m_{b}a=2\times 9.81-2\times 0.981=17.65N$

Tension in cable is $17.65N$ and acceleration is $0.98m/s^2$