Inclined Planes

Q.
A block of mass $m$ is pushed towards a movable wedge of mass $\eta m$ and height $h$, with a velocity $u$. All surfaces are smooth. The minimum value of $u$ for which the block will reach the top of the wedge is

1. $\sqrt{2gh}$
2. $\sqrt{2gh(1+\frac{1}{\eta })}$
3. $\sqrt{2gh(1-\frac{1}{\eta })}$
4. $\eta \sqrt{2gh}$

Q. What is the acceleration of the block?

1. $g$
2. $gcos\theta$
3. $gsin\theta$
4. $gtan\theta$

Q. Which will have the highest speed when it reaches the bottom of the incline?

1. 1
2. 2
3. 3
4. All 3 will have the same speed

Q. Which will reach first?

1. 2
2. 3
3. All 3 together
4. 1

Q.

A block is kept on a frictionless inclined surface with angle of inclination $\alpha$. The incline is given an acceleration a to keep the block stationary. Then $\alpha$ is equal to

(AIEE 2005)

1. g cosec

2. 

3. g tan

4. g

Q. will have the highest speed when it reaches the bottom of the incline.

1. All
2. 1
3. 2
4. 3

Q. The acceleration of the block will be .

1. $gcos\theta$
2. $gsin\theta$
3. $gtan\theta$
4. g

Q. will reach first.

1. All 3 together
2. 1
3. 2
4. 3

Q. In the arrangement shown in the figure $[\sin {37}^{\circ }=\frac{3}{5}]$

1. direction of force of friction is up the plane.
2. the magnitude of force of friction is zero.
3. the tension in the string is $20\text{N}$.
4. magnitude of force of friction is $56\text{N}$

Q. Two balls are placed as shown in the figure on a weightless support formed by two smooth inclined planes each of which forms an angle of $\alpha$ with the horizontal. The support can slide without friction along a horizontal plane. The upper ball of mass $m_1$ is released. Determine the condition under which the lower ball of mass $m_2$ starts climbing up the support.

1. $m_1\sin 2\alpha >m_2$
2. $m_1\cos 2\alpha >m_2$
3. $m_2\cos 2\alpha >m_1$
4. $m_1\cos 2\alpha >m_2$