Vector Components

Q. A gun fires a bullet of mass $50\text{g}$ with a velocity of $30\text{m/s}$. Due to this, the gun is pushed back with a velocity of $1\text{m/s}$, then the mass of the gun is:

1. $5.5\text{kg}$
2. $0.5\text{kg}$
3. $3.5\text{kg}$
4. $1.5\text{kg}$

Q. A particle moving in the $xy$ plane experiences a velocity dependent force $\overrightarrow{F}=k(v_y\hat{i}+v_x\hat{j}),$ where $v_x$ and $v_y$ are $x$ and $y$ components of its velocity $\overrightarrow{v}.$ If $\overrightarrow{a}$ is the acceleration of the particle, then which of the following statements is true for the particle?

1. Quantity $\overrightarrow{v}\times \overrightarrow{a}$ is constant in time
2. $\overrightarrow{F}$ arises due to a magnetic field
3. Kinetic energy of particle is constant in time
4. Quantity $\overrightarrow{v}.\overrightarrow{a}$ is constant in time

Q. A bullet of mass $5g$ is fired at a velocity $900m{s}^{-1}$ from a rifle of mass $2.5kg.$ What is recoil velocity of the rifle?

1. $0.9m{s}^{-1}$
2. $180m{s}^{-1}$
3. $1.8m{s}^{-1}$
4. $900m{s}^{-1}$

Q.

A machine gun of mass 12 kg fires 25 g bullets at the rate of 4 bullets per second with a velocity of 500 ms^-1. What force must be applied to the gun to hold it in position?

1. 20 N

2. 12.5 N

3. 50 N

4. 75 N

Q. An object is in equilibrium under four concurrent forces in the directions shown in figure. Find the magnitude of $F_1$ and $F_2$ (in $N$).

1. $4\sqrt{3}$ and $20\sqrt{3}$
2. $\frac{4}{\sqrt{3}}$ and $\frac{20}{\sqrt{3}}$
3. $4\sqrt{3}$ and $\frac{20}{\sqrt{3}}$
4. $\frac{4}{\sqrt{3}}$ and $20\sqrt{3}$

Q. An object is in equilibrium under four concurrent forces in the directions shown in figure. Find the magnitude of $F_1$ and $F_2$ (in $N$).

1. $4\sqrt{3}$ and $20\sqrt{3}$
2. $\frac{4}{\sqrt{3}}$ and $\frac{20}{\sqrt{3}}$
3. $4\sqrt{3}$ and $\frac{20}{\sqrt{3}}$
4. $\frac{4}{\sqrt{3}}$ and $20\sqrt{3}$

Q. Given $\overrightarrow{C}=\overrightarrow{A}\times \overrightarrow{B}$ and $\overrightarrow{D}=\overrightarrow{B}\times \overrightarrow{A}$, Then the angle between $\overrightarrow{C}$and $\overrightarrow{D}$ is.

1. ${60}^{\circ }$
2. ${60}^{\circ }$
3. ${120}^{\circ }$
4. ${180}^{\circ }$

Q. A bullet moving with a velocity $u$ passes through a block at rest and free to move. The two are of equal mass. After passing through the block, the velocity of the emerging bullet is $fu$. Its velocity relative to the block is :

1. $fu$
2. $(1-f)u$
3. $(2f-1)u$
4. $(2-f)u$

Q. A 50 g bullet moving with velocity 10 m/s strikes a block of mass 950 g at rest and gets embedded in it. The loss in kinetic energy will be

1. $100$%
2. $95$%
3. $5$%
4. $50$%

Q. A gun fires bullet of mass $50\text{g}$ with a velocity of $30\text{m/s}$. Due to this, the gun is pushed back with a velocity of $1\text{m/s}$, then the mass of the gun is

1. $1.5\text{kg}$
2. $0.5\text{kg}$
3. $5.5\text{kg}$
4. $3.5\text{kg}$

Q. A bullet is fired form a rifle. If the rifle recoils freely, then the kinetic energy of the rifle will be

1. Same as that of bullet
2. More than that of bullet
3. None of these
4. Less than that of bullet

Q. A body of mass $M$ moves with a velocity $V$ and collides elastically with a another body of mass $m(M\gg m)$ at rest then the velocity of body of mass $m$ is

1. $2V$
2. $V$
3. Zero
4. $V/2$

Q. A mass $m_1$ moves with a large velocity. It strikes another mass $m_2$ at rest in a head on collision. It comes back along its path with lesser speed after collision. Then

1. $m_1<m_2$
2. $m_1>m_2$
3. $m_1=m_2$
4. There is no relation between $m_1$ and $m_2$

Q. A particle of mass M explodes in the ratio 2:4:5 . The first moves with 4m/s second moves with 5m/s making angle 53 with first , find velocity of the third mass .

Q.

Vectors $\overrightarrow{C}$ and $\overrightarrow{D}$ have magnitudes of 3 and 4 units respectively. What is the angle between the directions of $\overrightarrow{C}$ and $\overrightarrow{D}$ if the magnitude of vector product $\overrightarrow{C}\times \overrightarrow{D}$ is x and y respectively?

(x) 0 (y) 12 units

(i) 0 (ii)$\frac{\pi }{2}$ (iii)$\frac{\pi }{3}$ (iv) $\frac{\pi }{4}$

1. (x) - (iv); (y) - (iii)

2. (x) - (i); (y) - (ii)

3. (x) - (ii); (y) - (i)

4. (x) - (i); (y) - (iv)

Q. A wooden block of mass $1950$ g is at rest on a smooth horizontal table. A bullet of mass $50$ g is fired into the block and gets embedded in it. The velocity with which the bullet strikes the block is ${100ms}^{-1}$; find their common velocity.

1. ${3.5ms}^{-1}$
2. ${0.625ms}^{-1}$
3. ${1.25ms}^{-1}$
4. ${2.5ms}^{-1}$

Q. Given $\overrightarrow{C}=\overrightarrow{A}\times \overrightarrow{B}$ and $\overrightarrow{D}=\overrightarrow{B}\times \overrightarrow{A}$, Then the angle between $\overrightarrow{C}$and $\overrightarrow{D}$ is.

1. ${60}^{\circ }$
2. ${60}^{\circ }$
3. ${120}^{\circ }$
4. ${180}^{\circ }$

Q. A gun fires a bullet of mass 50 gm with a velocity of $30mse{c}^{-1}$ because of this the gun is pushed back with a velocity of $1mse{c}^{-1}$ The mass of the gun is

1. $20kg$
2. $1.5kg$
3. $30kg$
4. $15kg$

Q. The angle between the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\theta$. The triple product $\overrightarrow{A}.(\overrightarrow{B}\times \overrightarrow{A})$ is equal to.

1. $A^{2}Bsi{n}^2\theta$
2. $A^{2}Bsin\theta cos\theta$
3. $A^{2}Bco{s}^2\theta$
4. \N

Q.

A $10g$ bullet traveling at $200m/s$ strikes and remains embedded in a $2kg$ target which is originally at rest but free to move. At what speed does the target move off?

Q. A bullet of mass a and velocity b is fired into a large block of wood of mass c. The final velocity of the system is

1. $\frac{b}{c}(a+b)$
2. $\frac{ab}{a+c}$
3. $\frac{b}{a}(a+c)$
4. $\frac{cb}{a+b}$