A system consists of three masses \(m_1\), \(m_2\), and \(m_3\) connected by a string passing over a pulley \(\mathrm{P}\). The mass \(m_1\) hangs freely, and \(m_2\) and \(m_3\) are on a rough horizontal table (the coefficient of friction = \(\mu\)). The pulley is frictionless and of negligible mass. The downward acceleration of mass \(m_1\) is: (Assume \(m_1=m_2=m_3=m\) and \(g\) is the acceleration due to gravity.)
1. \(\frac{g(1-g \mu)}{9}\)
2. \(\frac{2 g \mu}{3}\)
3. \( \frac{g(1-2 \mu)}{3}\)
4. \(\frac{g(1-2 \mu)}{2}\)
A block of mass \(\mathrm{m}\) is in contact with the cart C as shown in the figure.
The coefficient of static friction between the block and the cart is . The acceleration of the cart that will prevent the block from falling satisfies:
1.
2.
3.
4.
A block of mass m lying on a rough horizontal plane is acted upon by a horizontal force P and another force Q inclined at an angle θ to the vertical. The block will remain in equilibrium if the coefficient of friction between it and the surface is:
1.
2.
3.
4.
A plank with a box on it at one end is gradually raised at the other end. As the angle of inclination with the horizontal reaches 30°, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank, respectively, will be:
1. | 0.6 and 0.6 | 2. | 0.6 and 0.5 |
3. | 0.5 and 0.6 | 4. | 0.4 and 0.3 |
If between block A and inclined plane is 0.5 and that between block B and the inclined plane is 0.8, then the normal reaction between blocks A and B will be:
1. 180 N
2. 216 N
3. 0
4. None of these
Two blocks of masses 2 kg and 3 kg placed on a horizontal surface are connected by a massless string. If 3 kg is pulled by 10 N as shown in the figure, then the force of friction acting on the 2 kg block will be: [Take g = 10 ]
1. | 6 N | 2. | 4 N |
3. | 8 N | 4. | 12 N |