## Block A of mass m and block B of mass 2m are placed on a fixed triangular wedge by means of a light and inextensible string …

Q: Block A of mass m and block B of mass 2m are placed on a fixed triangular wedge by means of a light and inextensible string and a frictionless pulley as shown in figure. The wedge is inclined at 45° to the horizontal on both sides. The coefficient of friction between the block A and the wedge is 2/3 and that between the block B and the wedge is 1/3. If the system of A and B is released from rest, then the acceleration of A is

(a) 1.5 ms-2

(b) 0

(c) 0.5 ms-2

(d) 1 ms-2

Ans: (b)

(fmax)A = μA(m g cos45)

(fmax)B = μB(2m g cos45)

Hence , the maximum value of friction obtained is

fmax = (fmax)A + (fmax)B …(i)

Net pulling force on the system is

F = F1-F2

F = 2m g sin45 – mg sin45 …(ii)

Pulling force < fmax

Therefore, the system will not move or the acceleration of block A will be zero.

## Two blocks of masses m1 and m2 connected by a string and placed on an rough inclined plane having coefficient of friction…

Q: Two blocks of masses m1 and m2 connected by a string and placed on an rough inclined plane having coefficient of friction μas shown in figure. The ratio of masses m1/m2 so that the block m1 starts moving downward.

(a) $\displaystyle \frac{m_1}{m_2} \textgreater (\mu cos\theta - sin\theta )$

(b) $\displaystyle \frac{m_1}{m_2} \textgreater ( sin\theta +\mu cos\theta )$

(c) $\displaystyle \frac{m_1}{m_2} \textgreater ( cos\theta - \mu sin\theta )$

(b) $\displaystyle \frac{m_1}{m_2} \textgreater ( sin\theta -\mu cos\theta )$

Ans: (a)

Sol: $\displaystyle m_2 g sin\theta \textgreater \mu m_2 g cos\theta + m_1 g$

## A block slides down an inclined plane (angle of inclination 60°) with an acceleration g/2 ….

Q: A block slides down an inclined plane (angle of inclination 60°) with an acceleration g/2. The coefficient of kinetic (dynamic) friction.

(a) $\displaystyle \sqrt{3} + 1$

(b) $\displaystyle \sqrt{3} - 1$

(c) $\displaystyle \sqrt{2} + 1$

(d) $\displaystyle \sqrt{2} - 1$

Ans:(b)
Sol:
$\displaystyle mg sin\theta - f = m a$

$\displaystyle m gsin\theta - \mu mgcos\theta = mg/2$

$\displaystyle sin\theta - \mu cos\theta = 1/2$

$\displaystyle sin60 - \mu cos60 = 1/2$

on putting the value we get

$\displaystyle \mu = \sqrt{3}-1$

## A block of mass m = 3 kg slides on a rough inclined plane of coefficient of friction 0.2….

Q: A block of mass m = 3 kg slides on a rough inclined plane of coefficient of friction 0.2. The resultant force offered by the plane on the block.

(a) $\displaystyle 6\sqrt{13} N$

(b) $\displaystyle 6\sqrt{17} N$

(c) $\displaystyle 6\sqrt{15} N$

(d) $\displaystyle 6\sqrt{11} N$

Ans: (a)

Sol: (a) $\displaystyle \sqrt{N^2 + f^2}$

## Two blocks A and B each of mass 1 kg are on an inclined plane of inclination 37°. The coefficient of kinetic friction …..

Q: Two blocks A and B each of mass 1 kg are on an inclined plane of inclination 37°. The coefficient of kinetic friction between blocks and the inclined plane is µk = 0.5. At t = 0, block A is released from rest but block B is projected up along inclined plane with speed 10 m/s. The initial separation between blocks is 6 m. Find the distance from initial position of A, where they will collide.

(a) 1 m

(b) 2 m

(c) 3 m

(d) 4 m

Ans: (a)