Three different objects of masses $m_1, m_2$ and m₃ are allowed to fall from rest and from the same point ‘O’ along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio of 

(1) $m_1:m_2:m_3$

(2) $m_1:2m_2:3m_3$

(3) 1 : 1 : 1

(4) $\frac{1}{m_1}:\frac{1}{m_2}:\frac{1}{m_3}$ 

A sphere of mass m is tied to end of a string of length l and rotated through the other end along a horizontal circular path with speed v. The work done by centripetal force in full horizontal circle is 

(1) 0

(2) $\left(\frac{{\displaystyle m{v}^2}}{{\displaystyle l}}\right)\hspace{0.17em}.\hspace{0.17em}2\pi l$

(3) $\text{mg\hspace{0.17em}.\hspace{0.17em}2πl}$

(4) $\left(\frac{{\displaystyle m{v}^2}}{{\displaystyle l}}\right)\hspace{0.17em}.\hspace{0.17em}\left(l\right)$

A ball is suspended by a thread of length l. What minimum horizontal velocity has to be imparted to the ball for it to reach the height of the suspension:

(1) gl

(2) 2 gl

(3) $\sqrt{gl}$

(4) $\sqrt{2gl}$

Work done by a frictional force is

(1) Negative

(2) Positive

(3) Zero

(4) All of the above

A body moves a distance of 10 m along a straight line under the action of a force of 5 N. If the work done is 25 joules, the angle which the force makes with the direction of motion of the body is

(1) 0°

(2) 30°

(3) 60°

(4) 90°

A mass of 0.5kg moving with a speed of 1.5 m/s on a horizontal smooth surface, collides with a nearly weightless spring of force constant k = 50 N/m. The maximum compression of the spring would be 

(1) 0.15 m

(2) 0.12 m

(3) 1.5 m

(4) 0.5 m

A 0.5 kg ball is thrown up with an initial speed 14 m/s and reaches a maximum height of 8.0m. How much energy is dissipated by air drag acting on the ball during the ascent 

(1) 19.6 Joule

(2) 4.9 Joule

(3) 10 Joule

(4) 9.8 Joule

An ice cream has a marked value of 700 kcal. How many kilowatt- hour of energy will it deliver to the body as it is digested 

(1) 0.81 kWh

(2) 0.90 kWh

(3) 1.11 kWh

(4) 0.71 kWh

A particle of mass m at rest is acted upon by a force F for a time t. Its Kinetic energy after an interval t is 

(1) $\frac{F^2{t}^2}{m}$

(2) $\frac{F^2{t}^2}{2m}$

(3) $\frac{F^2{t}^2}{3m}$

(4) $\frac{Ft}{2m}$

A block of mass \(m\) initially at rest, is dropped from a height \(h\) onto a spring of force constant \(k.\) If the maximum compression in the spring is \(x,\) then:     
            
1. \(m g h = \frac{1}{2} k x^{2}\)
2. \(m g \left(h + x\right) = \frac{1}{2} k x^{2}\)
3. \(m g h = \frac{1}{2} k \left(x + h\right)^{2}\)
4. \(m g \left(h + x \right) = \frac{1}{2} k \left(x + h \right)^{2}\)${\mathrm{}}^{}$