Two blocks A and B of equal masses are slidin | vedclass

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

Question

(A) The acceleration of a block sliding down an inclined plane is given by $a = g(\sin 	heta - \mu \cos 	heta)$.For block $A$: $a_A = 10(\sin 45^{\c

Vedclass · Accepted Answer

$2 	ext{ s}, 8\sqrt{2} 	ext{ m}$

Vedclass · Answer

(A) The acceleration of a block sliding down an inclined plane is given by $a = g(\sin 	heta - \mu \cos 	heta)$.For block $A$: $a_A = 10(\sin 45^{\circ} - 0.2 \cos 45^{\circ}) = 10 	imes \frac{1}{\sqrt{2}}(1 - 0.2) = \frac{8}{\sqrt{2}} 	ext{ m/s}^2$.For block $B$: $a_B = 10(\sin 45^{\circ} - 0.3 \cos 45^{\circ}) = 10 	imes \frac{1}{\sqrt{2}}(1 - 0.3) = \frac{7}{\sqrt{2}} 	ext{ m/s}^2$.The relative acceleration of $A$ with respect to $B$ is $a_{AB} = a_A - a_B = \frac{8}{\sqrt{2}} - \frac{7}{\sqrt{2}} = \frac{1}{\sqrt{2}} 	ext{ m/s}^2$.Given the initial separation $s_{AB} = \sqrt{2} 	ext{ m}$,we use the equation of motion $s_{AB} = u_{AB}t + \frac{1}{2}a_{AB}t^2$. Since $u_{AB} = 0$,we have $\sqrt{2} = \frac{1}{2} 	imes \frac{1}{\sqrt{2}} 	imes t^2$.Solving for $t$: $t^2 = 4 \Rightarrow t = 2 	ext{ s}$.Now,the distance traveled by block $A$ from its initial position is $s_A = \frac{1}{2}a_A t^2 = \frac{1}{2} 	imes \frac{8}{\sqrt{2}} 	imes (2)^2 = \frac{1}{2} 	imes \frac{8}{\sqrt{2}} 	imes 4 = \frac{16}{\sqrt{2}} = 8\sqrt{2} 	ext{ m}$.

Similar Questions

The upper half of an inclined plane of inclination $\theta$ is perfectly smooth,while the lower half is rough. $A$ body starting from rest at the top comes back to rest at the bottom. The coefficient of friction $\mu$ for the lower half is given by:

$A$ block of mass $5 \, kg$ is placed on a rough inclined plane with an angle of $30^\circ$. If the block moves down with a constant velocity,what is the coefficient of friction? (Take $g = 10 \, m/s^2$)

When the angle of inclination of an inclined plane is $\theta$,an object slides down with uniform velocity. If the same object is pushed up with an initial velocity $u$ on the same inclined plane,it goes up the plane and stops at a certain distance on the plane. Thereafter,the body:

Vedclass Test Series

Exam Paper Generator

Online Exam Module