A body of mass $m_1$ moving with uniform velocity of 40 m/s collides with another mass $m_2$ at rest and then the two together begin to move with uniform velocity of 30 m/s. The ratio of their masses $\frac{m_1}{m_2}$ is

(1) 0.75

(2) 1.33

(3) 3.0

(4) 4.0

A ball of mass m moving with a speed u undergoes a head-on elastic collision with a ball of mass nm initially at rest. The fraction of initial energy transferred to the heavier ball is

(1) $\frac{n}{1+n}$

(2) $\frac{n}{{(1+n)}^2}$

(3) $\frac{2n}{{(1+n)}^2}$

(4) $\frac{4n}{{(1+n)}^2}$

A sphere of mass m moving horizontally with velocity $v_0$ collides against a pendulum bob of mass m. If the two masses stick together after the collision, then the maximum height attained is

(1) $\frac{v_0^2}{2g}$

(2) $\frac{v_0^2}{4g}$

(3) $\frac{v_0^2}{6g}$

(4) $\frac{v_0^2}{8g}$

An object of mass \(500\) g initially at rest is acted upon by a variable force whose x-component varies with \(x\) in the manner shown. The velocities of the object at the points \(x=8\) m and \(x=12\) m would have the respective values of nearly:

A body of mass 2 kg moving with a velocity of $(\hat{\mathrm{i}}+$ $2\hat{\mathrm{j}}-$ $3\hat{\mathrm{k}})$ ms${}^{-1}$ collides with another body of mass 3 kg moving with a velocity of $(2\hat{\mathrm{i}}+$ $\hat{\mathrm{j}}+$ $\hat{\mathrm{k}})$ ms${}^{-1}$ . If they stick together, the velocity in ms${}^{-1}$ of the composite body will be:

1. $\frac{1}{5}(8\hat{i}+$ $7\hat{j}-$ $3\hat{k})$

2. $\frac{1}{5}(-4\hat{i}+$ $\hat{j}-$ $3\hat{k})$

3. $\frac{1}{5}(8\hat{i}+\hspace{0.17em}\hat{\mathrm{j}}-$ $\hat{\mathrm{k}})$

4. $\frac{1}{5}(-4\hat{i}+$ $7\hat{j}-$ $3\hat{k})$

A body of mass 5 kg is moving with a velocity of 10 m/s. Now a force that delivers a constant power of 75 watts is applied to it for 10 s in the same direction. The velocity of the body after 10 s will be

1.  $10\sqrt{2} \mathrm{m}/\mathrm{s}$

2.  20 m/s

3.  40 m/s

4.  $25\sqrt{2}$m/s

A mass of 4kg falls from a height h on the pan. Initially, the spring is in its natural length and mass of spring and pan are negligible. Spring constant of the spring is 1000 N/m. The mass compresses the spring by 0.5 m. Then the height 'h' is

1.  2.00 m

2.  1.56 m

3.  4.0 m

4.  2.625 m

Human heartbeats 72 times per minute. It pumps 1 cc blood in each pulse under the pressure of $2 \times {10}^{{}^4 } \mathrm{N}/{\mathrm{m}}^2.$ The power of the heart is 

1.  0.2 watt

2.  0.02 watt 

3.  0.024 watt

4.  $2.2 \times {10}^{-1}$watt

A body having an initial kinetic energy 2 J collides with an identical body at rest. The maximum loss of kinetic energy in the collision will be:

A particle is thrown at an acute angle with the horizontal. Select the incorrect statement.