Momentum, Newton's second law and impulse — NEET & JEE Questions

Question 1 · difficulty L1 · recall

Linear momentum of a particle is defined as

• A. $\vec p=m\vec v$
• B. $\vec p=m\vec a$
• C. $\vec p=\vec F/m$
• D. $\vec p=m/\vec v$

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

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 5 · 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 6 · 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 7 · 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 8 · 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. $${\overrightarrow {p'} _1} = {a_1}\widehat i + {b_1}\widehat j;{\overrightarrow {p'} _2} = {a_2}\widehat i + {b_1}\widehat j$$

Question 9 · difficulty L3 · understanding

In the given arrangement of a doubly inclined plane two blocks of masses $$M$$ and $$m$$ are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0.25. The value of $$m$$, for which $$M=10 \mathrm{~kg}$$ will move down with an acceleration of $$2 \mathrm{~m} / \mathrm{s}^2$$, is: (take $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$ and $$\left.\tan 37^{\circ}=3 / 4\right)$$

• A. 4.5 kg
• B. 6.5 kg
• C. 9 kg
• D. 2.25 kg

Question 10 · difficulty L3 · understanding

As per given figure, a weightless pulley P is attached on a double inclined frictionless surfaces. The tension in the string (massless) will be (if g = 10 m/s$$^2$$)

• A. $$\left( {4\sqrt 3 - 1} \right)N$$
• B. $$\left( {4\sqrt 3 + 1} \right)N$$
• C. $$4\left( {\sqrt 3 - 1} \right)N$$
• D. $$4\left( {\sqrt 3 + 1} \right)N$$