Momentum, Newton's second law and impulse — practice questions

Question 1 · difficulty L2 · understanding

Three blocks $$\mathrm{M_1, M_2, M_3}$$ having masses $$4 \mathrm{~kg}, 6 \mathrm{~kg}$$ and $$10 \mathrm{~kg}$$ respectively are hanging from a smooth pully using rope 1, 2 and 3 as shown in figure. The tension in the rope $$\mathrm{1, T_1}$$ when they are moving upward with acceleration of $$2 \mathrm{~ms}^{-2}$$ is __________ $$\mathrm{N}$$ (if $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$).

Question 2 · difficulty L2 · understanding

A light unstretchable string passing over a smooth light pulley connects two blocks of masses $$m_1$$ and $$m_2$$. If the acceleration of the system is $$\frac{g}{8}$$, then the ratio of the masses $$\frac{m_2}{m_1}$$ is :

• A. $$5: 3$$
• B. $$8: 1$$
• C. $$9: 7$$
• D. $$4: 3$$

Question 3 · difficulty L2 · understanding

A light string passing over a smooth light pulley connects two blocks of masses $$m_1$$ and $$m_2\left(\right.$$ where $$\left.m_2>m_1\right)$$. If the acceleration of the system is $$\frac{g}{\sqrt{2}}$$, then the ratio of the masses $$\frac{m_1}{m_2}$$ is:

• A. $$\frac{1+\sqrt{5}}{\sqrt{5}-1}$$
• B. $$\frac{\sqrt{3}+1}{\sqrt{2}-1}$$
• C. $$\frac{\sqrt{2}-1}{\sqrt{2}+1}$$
• D. $$\frac{1+\sqrt{5}}{\sqrt{2}-1}$$

Question 4 · difficulty L2 · understanding

Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is 0.04 , the acceleration of the system in $\mathrm{ms}^{-2}$ is : (Consider that the string is massless and unstretchable and the pulley is also massless and frictionless) :

• A. 1.2
• B. 4
• C. 3
• D. 2

Question 5 · difficulty L2 · understanding

A light string passing over a smooth light fixed pulley connects two blocks of masses $$m_1$$ and $$m_2$$. If the acceleration of the system is $$g / 8$$, then the ratio of masses is:

• A. $$\frac{8}{1}$$
• B. $$\frac{9}{7}$$
• C. $$\frac{5}{3}$$
• D. $$\frac{4}{3}$$

Question 6 · difficulty L2 · understanding

Three blocks $$A, B$$ and $$C$$ are pulled on a horizontal smooth surface by a force of $$80 \mathrm{~N}$$ as shown in figure The tensions T$$_1$$ and T$$_2$$ in the string are respectively :

• A. 40N, 64N
• B. 60N, 80N
• C. 80N, 100N
• D. 88N, 96N

Question 7 · difficulty L2 · understanding

Two masses $$M_{1}$$ and $$M_{2}$$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $$M_{2}$$ is twice that of $$M_{1}$$, the acceleration of the system is $$a_{1}$$. When the mass $$M_{2}$$ is thrice that of $$M_{1}$$, the acceleration of the system is $$a_{2}$$. The ratio $$\frac{a_{1}}{a_{2}}$$ will be :

• A. $$\frac{1}{3}$$
• B. $$\frac{2}{3}$$
• C. $$\frac{3}{2}$$
• D. $$\frac{1}{2}$$

Question 8 · difficulty L3 · understanding

A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m 2 /s. The kinetic energy of the pendulum just after the lift-off is K Joules. The value of J is ___________.

Question 9 · difficulty L3 · understanding

A block of mass $5 \mathrm{~kg}$ moves along the $x$-direction subject to the force $F=(-20 x+10) \mathrm{N}$, with the value of $x$ in metre. At time $t=0 \mathrm{~s}$, it is at rest at position $x=1 \mathrm{~m}$. The position and momentum of the block at $t={\pi \over 4} \mathrm{s}$ are

• A. $-0.5 \mathrm{~m}, 5 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$
• B. $0.5 \mathrm{~m}, 0 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$
• C. $0.5 \mathrm{~m},-5 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$
• D. $-1 \mathrm{~m}, 5 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$

Question 10 · difficulty L3 · understanding

Two balls, having linear momenta $${\overrightarrow p _1} = p\widehat i$$ and $${\overrightarrow p _2} = - p\widehat i$$, undergo a collision in free space. There is no external force acting on the balls. Let $${\overrightarrow {p'} _1}$$ and $${\overrightarrow {p'} _2}$$ be their final momenta. The following option(s) is (are) NOT ALLOWED for any non-zero value of $$p,{a_1},{a_2},{b_1},{b_2},{c_1}$$ and $${c_2}$$ :

• A. $${\overrightarrow {p'} _1} = {a_1}\widehat i + {b_1}\widehat j + {c_1}\widehat k;{\overrightarrow {p'} _2} = {a_2}\widehat i + {b_2}\widehat j$$
• B. $${\overrightarrow {p'} _1} = {c_1}\widehat k;{\overrightarrow {p'} _2} = {c_2}\widehat k$$
• C. $${\overrightarrow {p'} _1} = {a_1}\widehat i + {b_1}\widehat j + {c_1}\widehat k;{\overrightarrow {p'} _2} = {a_2}\widehat i + {b_2}\widehat j - {c_1}\widehat k$$
• D. $${\overrightarrow {p'} _1} = {a_1}\widehat i + {b_1}\widehat j;{\overrightarrow {p'} _2} = {a_2}\widehat i + {b_1}\widehat j$$