A small wooden cube is placed on a plank. The | vedclass

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

Question

(C) Concept: The wooden cube will leave the plank at the top extreme position if the downward acceleration of the plank exceeds the acceleration due t

Vedclass · Accepted Answer

$\frac{5}{18} 	ext{ m}$

Vedclass · Answer

(C) Concept: The wooden cube will leave the plank at the top extreme position if the downward acceleration of the plank exceeds the acceleration due to gravity.For the block not to leave the plank,the normal force $N$ must be greater than or equal to zero.From the free body diagram of the block,the equation of motion is: $mg - N = ma$.For the block to remain in contact,$N \geq 0$,which implies $mg \geq ma$,or $a \leq g$.In $S$.$H$.$M$.,the maximum acceleration is given by $a_{max} = \omega^2 A$.Therefore,the condition for the block not to leave the plank is $\omega^2 A \leq g$,or $A \leq \frac{g}{\omega^2}$.Given frequency $f = \frac{3}{\pi} 	ext{ Hz}$.Angular frequency $\omega = 2\pi f = 2\pi \left( \frac{3}{\pi} ight) = 6 	ext{ rad/s}$.Substituting the values: $A \leq \frac{10}{6^2} = \frac{10}{36} = \frac{5}{18} 	ext{ m}$.Thus,the maximum amplitude is $\frac{5}{18} 	ext{ m}$.

$A$ small wooden cube is placed on a plank. The plank performs a vertical $S$.$H$.$M$. of frequency $\frac{3}{\pi} \text{ Hz}$. The maximum amplitude of the plank so that the wooden block does not leave the plank is [take $g = 10 \text{ m/s}^2$].

Similar Questions

$A$ particle is executing simple harmonic motion with an amplitude of $0.1 \, m$. At a certain instant when its displacement is $0.02 \, m$,its acceleration is $0.5 \, m/s^2$. The maximum velocity of the particle is (in $m/s$):

The acceleration of a particle executing $SHM$ is

Acceleration of a particle,executing $SHM$,at its mean position is

$A$ body is executing $S.H.M.$ under the action of a force having a maximum magnitude of $50 \,N$. When its energy is half kinetic and half potential, the magnitude of the force acting on the particle is:

In simple harmonic motion,the ratio of acceleration of the particle to its displacement at any time is a measure of

Vedclass Test Series

Exam Paper Generator

Online Exam Module