A block of mass m slides down on a wedge of m | vedclass

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

Question

(D) $1$. For the wedge of mass $M$,the horizontal force is provided by the horizontal component of the normal reaction $N_1$. The horizontal component

Vedclass · Accepted Answer

$m\vec a_2 = -M\vec a_1$

Vedclass · Answer

(D) $1$. For the wedge of mass $M$,the horizontal force is provided by the horizontal component of the normal reaction $N_1$. The horizontal component of $N_1$ is $N_1 \sin 	heta$. Thus,$N_1 \sin 	heta = M|\vec a_1|$. This confirms option $C$ is correct.$2$. For the block of mass $m$,the equation of motion perpendicular to the inclined surface is $mg \cos 	heta - N_1 = m a_{1y}$,where $a_{1y}$ is the vertical component of the block's acceleration relative to the wedge. Resolving the acceleration,we find $N_1 = m(g \cos 	heta - |\vec a_1| \sin 	heta)$. This confirms option $B$ is correct.$3$. For the entire system,the vertical acceleration of the center of mass is downward. Thus,the normal force $N_2$ from the ground must be less than the total weight $(M+m)g$. This confirms option $A$ is correct.$4$. The center of mass of the system moves only due to external forces. The horizontal external force on the system is zero. Therefore,the horizontal acceleration of the center of mass is zero: $M\vec a_1 + m\vec a_{2x} = 0$. Option $D$ states $m\vec a_2 = -M\vec a_1$,which implies the block's total acceleration is related to the wedge's acceleration in a way that ignores the relative motion component. This is incorrect.

Similar Questions

$A$ force $F = 10t$ acts on a block of mass $10 \, kg$ as shown in the figure. Find the time $t$ when the block loses contact with the surface.

$A$ cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is

Three blocks of masses $3\, kg, 2\, kg$,and $1\, kg$ are placed side by side on a smooth surface as shown in the figure. $A$ horizontal force of $12\, N$ is applied to the $3\, kg$ block. The net force on the $2\, kg$ block is ............ $N$.

With what minimum acceleration can a fireman slide down a rope if the breaking strength of the rope is $\frac{2}{3}$ of his weight?

$A$ smooth right-angled wedge of mass $M$ is kept on a smooth horizontal surface as shown. $A$ mass $m$ is released from the top of the wedge. When $m$ reaches the ground, its speed is $V$. Find the work done by the normal contact force on $m$ while it comes down to the ground.

Vedclass Test Series

Exam Paper Generator

Online Exam Module