In the figure shown,both blocks are released | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the mass of block $A$ be $m_A = 4 \ kg$ and block $B$ be $m_B = 1 \ kg$. The initial vertical separation between their bottom edges is $6 \ m$

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) Let the mass of block $A$ be $m_A = 4 \ kg$ and block $B$ be $m_B = 1 \ kg$. The initial vertical separation between their bottom edges is $6 \ m$ (based on the geometry of the system).From the Free Body Diagram $(FBD)$ of the blocks:For block $A$: $m_A g - T = m_A a \implies 4g - T = 4a \quad \dots(1)$For block $B$: $T - m_B g = m_B a \implies T - 1g = 1a \quad \dots(2)$Adding equations $(1)$ and $(2)$: $3g = 5a \implies a = \frac{3g}{5} = \frac{3 	imes 10}{5} = 6 \ m/s^2$.The acceleration of block $A$ relative to block $B$ is $a_{rel} = a - (-a) = 2a = 2 	imes 6 = 12 \ m/s^2$.To cross each other,the relative displacement required is $s_{rel} = 6 \ m$.Using the equation of motion $s = ut + \frac{1}{2}at^2$ with $u = 0$:$6 = 0 + \frac{1}{2} 	imes 12 	imes t^2$$6 = 6t^2 \implies t^2 = 1 \implies t = 1 \ s$.

In the figure shown,both blocks are released from rest. Find the time taken for them to cross each other. (Assume $g = 10 \ m/s^2$)

Similar Questions

Two masses $8\; kg$ and $12\; kg$ are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses and the tension in the string when the masses are released.

Three blocks of mass $5 \ kg$ each are suspended from a ceiling as shown in the figure. The value of $\frac{T_3}{T_1}$ is .............

$A$ light unstretchable string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$. If the acceleration of the system is $\frac{g}{8}$,then the ratio of the masses $\frac{m_2}{m_1}$ is:

Two blocks of masses $m$ and $M$ are connected by means of a metal wire of cross-sectional area $A$ passing over a frictionless fixed pulley as shown in the figure. The system is then released. If $M = 2m$,then the stress produced in the wire is

In order to raise a mass of $100\,kg$,a man of mass $60\,kg$ fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration $5g/4$ relative to the rope. The tension in the rope is ....... $N$. $(g = 10\,m/s^2)$

Vedclass Test Series

Exam Paper Generator

Online Exam Module