In the figure, the coefficient of friction between the floor and body B is 0.1. The coefficient of friction between bodies B and A is 0.2. A force F is applied as shown on B. The mass of A is rn/2 and of B is m.

Which of the following statement(s) is/are true?

1. (a, b, d, e)

2. (a, c, d, e)

3. (b, c, d)

4. (a, b, c)

Mass ${\mathrm{m}}_1$ moves on a slope making an angle $\mathrm{\theta }$ with the horizontal and is
attached to mass ${\mathrm{m}}_2$ by a string passing over a frictionless pulley as
shown in the figure. The coefficient of friction between ${\mathrm{m}}_1$ and the sloping
surface is $\mathrm{\mu }$.

$\begin{array}{l}\text{(a) If }{\mathrm{m}}_2>{\mathrm{m}}_1\sin \mathrm{\theta }\text{, the body will move up the plane.}\end{array}$
(b) If m₂>m₁(sin⁡θ+μcos⁡θ), the body will move up the plane.
(c) If m₂<m₁(sin⁡θ+μcos⁡θ), the body will move up the plane.
(d) If m₂<m₁(sin⁡θ−μcos⁡θ), the body will move down the plane.

Which of the following statement/s is/are true?

1. (a, d)

2. (a, c)

3. (c, d)

4. (b, d)

In figure a body A of mass m slides on a plane inclined at angle ${\mathrm{\theta }}_1$ to the horizontal and g is the coefficient of friction between A and the plane. A is connected by a light string passing over a frictionless pulley to another body B, also of mass m, sliding on a frictionless plane inclined at an angle ${\mathrm{\theta }}_2$ to the horizontal.

(a) A will never move up the plane
(b) A will just start moving up the plane when $\mathrm{\mu }=\frac{\sin {\mathrm{\theta }}_2-\sin {\mathrm{\theta }}_1}{\cos {\mathrm{\theta }}_1}$
(c) For A to move up the plane, ${\mathrm{\theta }}_2$ must always be greater than ${\mathrm{\theta }}_1$
(d) B will always slide down with a constant speed

Which of the following statement/s is/are true?

1. (b, c)
2. (c, d)
3. (a, c)
4. (a, d)