Acceleration

Q. Find the acceleration of the system shown in the figure.

1. $\frac{2g}{7}$
2. $\frac{g}{7}$
3. $\frac{2g}{3}$
4. $\frac{g}{4}$

Q. A particle is moving in the $x-y$ plane. At certain instant of time, the components of its velocity and acceleration are as follows: $v_x=3{\text{ms}}^{-1},v_y=4{\text{ms}}^{-1},a_x=2{\text{ms}}^{-2}$ and $a_y=1{\text{ms}}^{-2}$. The rate of change of speed at this moment is

1. $\sqrt{10}{\text{ms}}^{-2}$
2. $4{\text{ms}}^{-2}$
3. $\sqrt{5}{\text{ms}}^{-2}$
4. $2{\text{ms}}^{-2}$

Q. The system is released from rest. Derive the relation between acceleration of the masses involved.

1. $a_2=2a_1$
2. $a_2=a_1$
3. $a_1=2a_2$
4. $a_1=4a_2$

Q. A light string fixed at one end to a clamp on the ground passes over a fixed pulley and hangs at the other side. It makes an angle of ${30}^{\circ }$ with the ground. A monkey of mass $5\text{kg}$ climbs up the rope. The clamp can tolerate a vertical force of $40\text{N}$ only. The maximum acceleration in upward direction with which the monkey can climb safely is (neglect friction and take $g=10{\text{m/s}}^2$)

1. $2{\text{m/s}}^2$
2. $4{\text{m/s}}^2$
3. $8{\text{m/s}}^2$
4. $6{\text{m/s}}^2$

Q. In the figure shown, all pulleys are massless and the strings are light. What is the acceleration of the block $m$ of mass $10kg$? (All surfaces are smooth and take $g=10m/s^2$.)

1. $5{\text{m/s}}^2$ down the plane
2. $5{\text{m/s}}^2$ up the plane
3. $4.5{\text{m/s}}^2$ down the plane
4. $4.5{\text{m/s}}^2$ up the plane

Q. In the system shown, mass of block A, B and C are $m_A=4m,m_B=3m$ and $m_C=8m$. If the system is released from rest, find the acceleration of block $B$. Assume all surfaces to be smooth and string inextensible.

1. $\frac{g}{8}$
2. $\frac{g}{2}$
3. $\frac{g}{4}$
4. $g$

Q. Find the acceleration of block of mass $m$ w.r.t ground if acceleration of $M$ is $b=4m/s^2$. (Assume all surfaces to be smooth and string inextensible.)

1. $2m/s^2$
2. $3m/s^2$
3. $4m/s^2$
4. $1m/s^2$

Q. Two blocks with masses $m_1=3\text{kg}$ and $m_2=4\text{kg}$ are touching each other on a fricionless surface. If a force of $5\text{N}$ is applied on $m_1$ as shown in figure. The acceleration of each block is

1. $a_1=\frac{5}{7}{\text{m/s}}^2,a_2=\frac{5}{4}{\text{m/s}}^2$
2. $a_1=\frac{5}{3}{\text{m/s}}^2,a_2=\frac{5}{4}{\text{m/s}}^2$
3. $a_1=\frac{5}{4}{\text{m/s}}^2,a_2=\frac{5}{3}{\text{m/s}}^2$
4. $a_1=\frac{5}{7}{\text{m/s}}^2,a_2=\frac{5}{7}{\text{m/s}}^2$

Q. If the pulley is massless and moves with an upward acceleration $a_o$, find the acceleration of block $m_1$ w.r.t elevator.

1. $\frac{(m_2-m_1)a_o}{m_1}$
2. $\frac{(m_2-m_1)(g-a_o)}{(m_1+m_2)}$
3. $\frac{(m_2-m_1)(g+a_o)}{(m_1+m_2)}$
4. $\frac{(m_2-m_1)g}{m_1}$

Q. A $5\text{kg}$ block has a rope of mass $2\text{kg}$ attached to its underside and a $3\text{kg}$ block is suspended from the other end of the rope. The whole system is accelerated upward at $2{\text{ms}}^{-2}$ by an external force $F_0$.

What is the tension at middle point of the rope and $F_0$? $(g=10{\text{ms}}^{-2})$

1. $100\text{N},120\text{N}$
2. $20\text{N},100\text{N}$
3. $48\text{N},100\text{N}$
4. $48\text{N},120\text{N}$