In the figure,the mass of a ball is frac{9}{5 | vedclass

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

Question

(A) Let $a_{1}$ and $a_{2}$ be the accelerations of the ball (upward) and the rod (downward),respectively.From the constraint relation,$2 a_{1} = a_{2

Vedclass · Accepted Answer

$1.4$

Vedclass · Answer

(A) Let $a_{1}$ and $a_{2}$ be the accelerations of the ball (upward) and the rod (downward),respectively.From the constraint relation,$2 a_{1} = a_{2} \dots (i)$For the ball,the equation of motion is: $2T - \frac{9}{5}mg = \frac{9}{5}ma_{1} \dots (ii)$For the rod,the equation of motion is: $mg - T = ma_{2} \dots (iii)$Substituting $T = mg - ma_{2}$ from $(iii)$ into $(ii)$:$2(mg - ma_{2}) - \frac{9}{5}mg = \frac{9}{5}ma_{1}$$2mg - 2ma_{2} - 1.8mg = 1.8ma_{1}$$0.2g - 2a_{2} = 1.8a_{1}$Using $a_{2} = 2a_{1}$ from $(i)$:$0.2g - 2(2a_{1}) = 1.8a_{1}$$0.2g = 5.8a_{1} \implies a_{1} = \frac{0.2g}{5.8} = \frac{g}{29} \, m/s^2$ (upward)Then $a_{2} = 2a_{1} = \frac{2g}{29} \, m/s^2$ (downward)The relative acceleration of the ball with respect to the rod is $a_{rel} = a_{1} + a_{2} = \frac{g}{29} + \frac{2g}{29} = \frac{3g}{29}$.Using the equation of motion $s = ut + \frac{1}{2}a_{rel}t^2$ with $u=0$ and $s=1 \, m$:$1 = 0 + \frac{1}{2} \left(\frac{3 	imes 10}{29}ight) t^2$$1 = \frac{15}{29} t^2 \implies t^2 = \frac{29}{15} \approx 1.933$$t = \sqrt{1.933} \approx 1.39 \, s \approx 1.4 \, s$.

In the figure,the mass of a ball is $\frac{9}{5}$ times the mass of the rod. The length of the rod is $1 \, m$. The initial level of the ball is the same as the lower end of the rod. Find the time taken by the ball to reach the upper end of the rod. (in $s$)

Similar Questions

One end of a massless rope,which passes over a massless and frictionless pulley $P$,is tied to a hook while the other is free. The maximum tension the rope can bear is $360 \ N$. With what value of maximum safe acceleration (in $m \ s^{-2}$) can a man of $60 \ kg$ climb on the rope?

$A$ light spring balance hangs from the hook of another light spring balance,and a block of mass $M \, kg$ hangs from the lower one. Which of the following statements is true regarding the scale readings?

In the case of a wire having negligible mass,suspended from a ceiling and stretched under the action of a weight $F$ suspended from its other end,the tension at any cross-section of the wire is

In the adjoining figure,the tension in the string connecting blocks $A$ and $B$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module