Power, Force and Velocity

Q.

A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_c$ is varying with time $t$ as, $a_c=k^{2}r{t}^2$ , The power delivered to the particle by the forces acting on it is

1. 

2. 

3. 

4. Zero

Q.

A pump on the ground floor of a building can pump up water to fill a tank of volume 30 $m^3$ in 15 min. If the tank is 40 m above the ground, and the efficiency of the pump is 30%, how much electric power is consumed by the pump?

Q. A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time t is proportional to (i) t⅟² (ii) t (iii) t³/² (iv) t²

Q. A motor can pump the water upto maximum height of 10m at the rate of 10 kg per sec. If efficiency of the motor is 0.8 then power of motor i

Q.

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. 0.82 kWh

2. 0.90 kWh

3. 1.11 kWh

4. 0.71 kWh

Q. When a belt moves horizontally at a constant speed of $1.5{\text{ms}}^{-1},$ gravels are falling on it at rate of $5$ ${\text{kg s}}^{-1}.$ Then, the extra power required to drive the belt is

1. $11.25\text{W}$
2. $37.5\text{W}$
3. $7.5\text{W}$
4. $0.75\text{W}$

Q. A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time t is proportional to (i) t⅟² (ii) t (iii) t³́² (iv) t²

Q. A mass m falls from rest under the influence of gravity. Then the average power supplied to the mass by the force of gravity is

1. $P=m\sqrt{\frac{g^{3}h}{3}}$
2. $P=m\sqrt{\frac{g^{3}h}{12}}$
3. $P=2m\sqrt{\frac{g^{3}h}{2}}$
4. $P=m\sqrt{\frac{g^{3}h}{2}}$
   where h is the distance the mass falls.

Q. A force $F$ acting on a particle depends on displacement as $F\propto x^n$. Then, power delivered by the force depends on $x$ as:

1. $x^n$
2. $x^{(2n+1)}$
3. $x^{\frac{3n+1}{2}}$
4. $x^{\frac{5n+2}{2}}$

Q. A block of mass $2.0\text{kg}$ is pulled up on a smooth incline of angle ${30}^{\circ }$ with the horizontal. If the block moves with an acceleration of $1.0{\text{m/s}}^2$, then the power delivered by the pulling force at a time $4.0\text{s}$ and the average power delivered during the $4.0\text{s}$ after the motion starts are

1. $36W,24W$
2. $24W,24W$
3. $24W,12W$
4. $48W,24W$

Q. A one kilowatt motor pumps out water from a $\text{10 m}$ deep well. Calculate the quantity of water pumped out per second.(Take $g=10\text{m}/{\text{s}}^2$)

1. $\text{10 kg}$
2. $\text{8.96 kg}$
3. $\text{14.3 kg}$
4. $\text{9.8 kg}$

Q. A Force $\overrightarrow{F}=(6\hat{i}+4\hat{j}-2\hat{k})\text{N}$ is applied on a block which is moving with velocity $\overrightarrow{v}=(8\hat{i}+12\hat{j}-3\hat{k})\text{m/s}$. The instantaneous power applied to the particle is

1. $96\text{W}$
2. $102\text{W}$
3. $108\text{W}$
4. $90\text{W}$

Q. A car of 100 HP is moving with a constant velocity of 72 km/hour. The forward force exerted by the engine of the car is

1. $3.73\times {10}^{3}N$
2. $3.72\times {10}^{2}N$
3. $3.73\times {10}^{1}N$
4. $Noneoftheabove$

Q. A stone is projected at time t = 0 with a speed $v_0$ and an angle $\theta$ with the horizontal in a uniform gravitational field. The rate of work done (P) by the gravitational force plotted against time (t) will be as

1. 
2. 
3. 
4. 

Q. A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time t is proportional to

1. t
2. $t^{1/2}$
3. $t^{3/2}$
4. $t^2$

Q.

An electric motor creates a tension of 4500 N in a hoisting cable and reels it in at the rate of 2 m/s. What is the power of the electric motor?

1. 225 W

2. 900 W

3. 9 kW

4. 15 kW

Q. A constant power $P$ is applied to a particle of mass $m$. The distance travelled by the particle when its velocity increases from $v_1\text{to}{v}_2$ is - (neglect friction)

1. $\frac{3P}{m}(v_2^2-v_1^2)$
2. $\frac{m}{3P}(v_2-v_1)$
3. $\frac{m}{3P}(v_2^3-v_1^3)$
4. $\frac{m}{3P}(v_2^2-v_1^2)$

Q. A $40\text{kg}$ girl is swinging on a swing from rest. Then, the power delivered when moving with a velocity of $2\text{m/s}$ upwards in a direction making an angle ${60}^{\circ }$ with the vertical is

1. $248\sqrt{3}\text{W}$
2. $392\sqrt{3}\text{W}$
3. $448\text{W}$
4. $580\text{W}$

Q. A block of mass $2.0\text{kg}$ is pulled up on a smooth incline of angle ${30}^{\circ }$ with the horizontal. If the block moves with an acceleration of $1.0{\text{m/s}}^2$, then the power delivered by the pulling force at a time $4.0\text{s}$ and the average power delivered during the $4.0\text{s}$ after the motion starts are

1. $36W,24W$
2. $24W,24W$
3. $24W,12W$
4. $48W,24W$

Q. A particle $A$ of mass $\frac{10}{7}\text{kg}$ is moving in the positive $x-$ direction. Its initial position is $x=0$ and initial velocity is $1\text{m/s}$. The velocity at $x=10\text{m}$ in $\text{m/s}$ (use the graph given). Answer the nearest integer.

Q. If a force \(\overrightarrow{F}\ = (7~\hat{i} - 6~\hat{j} + 2~ \hat{k})~\text{N}\) and velocity \(\overrightarrow{v} = (6 ~\hat{i} + \hat{k}) ~\text{m/s}, \) then the instantaneous power is

Q. Power supplied to a particle of mass 2 kg varies with time as $p=\frac{3t^2}{2}$ watt. Here 't' is in second. If velocity of particle at t = 0 is v = 0. The velocity of particle at time t = 2 second will be

1. 1 m/s
2. 4 m/s
3. 2 m/s
4. $2\sqrt{2}m/s$

Q. A ball of mass $5\text{kg}$ is dropped from a tower. Find the power of gravitational force at time $t=2\text{seconds}$.
(Take $g=10{\text{m/s}}^2$)

1. $1000\text{W}$
2. $200\text{W}$
3. $100\text{W}$
4. $2000\text{W}$

Q. A cyclist is riding with a speed of 27 km/h. As he approaches a circular turn on the road of radius 80 m, he applies brakes and reduces his speed at the constant rate of 0.50 m/s every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn ?

Q. A particle moves with a velocity $5\overline{i}-3\overline{j}+6\overline{k}$ m/s under the influence of a constant force $\overrightarrow{F}=(10\overline{i}+10\overline{j}+20\overline{k})$N. The instantaneous power applied to the particle is

1. 200 J/S
2. 40 J/S
3. 140 J/S
4. 170 J/S

Q. A boy whose mass is $30\text{kg}$ climbs with a constant speed on a vertical rope of $6\text{m}$ length in $10\text{s}$. The power of the boy during the climb is
(Take $g=10{\text{m/s}}^2)$

1. $60\text{W}$
2. $3000\text{W}$
3. $180\text{W}$
4. $5\text{W}$

Q. A $50\text{N}$ force is applied to the body of $2\text{kg}$. This applied force maintains the velocity of the body at $2\text{m/s}$. If the body moves in perpendicular direction to the applied force, find the power delivered by the force.

1. $100\text{W}$
2. $0\text{W}$
3. $50\text{W}$
4. $200\text{W}$