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Work Power and Energy

505 Questions Start Allen Test
All Exams Allen Objective Errorless
Pb. PMT 2002; J & K CET 2004 Q251 Errorless Conservation of Energy and Momentum MCQ
A body moving with velocity v has momentum and kinetic energy numerically equal. What is the value of v
A.
2m/s
B.
$\sqrt{2}$ m/s
C.
1m/s
D.
0.2 m/s
JIPMER 2002 Q252 Errorless POWER MCQ
A pump motor is used to deliver water at a certain rate from a given pipe. To obtain twice as much water from the same pipe in the same time, power of the motor has to be increased to
A.
16 times
B.
4 times
C.
8 times
D.
2 times
Kerala PET 2002 Q253 Errorless POWER MCQ
A quarter horse power motor runs at a speed of 600 r.p.m. Assuming 40% efficiency the work done by the motor in one rotation will be
A.
7.46 J
B.
7400 J
C.
7.46 ergs
D.
74.6 J
Kerala PET 2002; CBSE PMT (Mains) 2010 Q254 Errorless POWER MCQ
A particle of mass M starting from rest undergoes uniform acceleration. If the speed acquired in time T is V, the power delivered to the particle is
A.
$\frac{MV^{2}}{T}$
B.
$\frac{1}{2}\frac{MV^{2}}{T^{2}}$
C.
$\frac{MV^{2}}{T^{2}}$
D.
$\frac{1}{2}\frac{MV^{2}}{T}$
Kerala PET 2002; EAMCET 2009 Q255 Errorless Elastic and Inelastic Collision MCQ
A body of mass 2kg makes an elastic collision with another body at rest and continues to move in the original direction with one fourth of its original speed. The mass of the second body which collides with the first body is
A.
2 kg
B.
1.2 kg
C.
3 kg
D.
1.5 kg
AFMC 2002; RPMT 2003 Q256 Errorless Elastic and Inelastic Collision MCQ
Two masses $m_A$ and $m_B$ moving with velocities $v_A$ and $v_B$ in opposite directions collide elastically. After that the masses $m_A$ and $m_B$ move with velocity $v_B$ and $v_A$ respectively. The ratio $(m_A / m_B)$ is
A.
1
B.
$\frac{v_A - v_B}{v_A + v_B}$
C.
$(m_A + m_B) / m_A$
D.
$v_A / v_B$
Kerala PMT 2002; MP PET 2002; WB-JEE 2013 Q257 Errorless Perfectly Inelastic Collision MCQ
A bullet of mass m moving with velocity v strikes a block of mass M at rest and gets embedded into it. The kinetic energy of the composite block will be
A.
$\frac{1}{2}mv^{2}\times\frac{m}{(m+M)}$
B.
$\frac{1}{2}mv^{2}\times\frac{M}{(m+M)}$
C.
$\frac{1}{2}mv^{2}\times\frac{(M+m)}{M}$
D.
$\frac{1}{2}Mv^{2}\times\frac{m}{(m+M)}$
IIT-JEE (Screening) 2002; DCE 2006 Q258 Errorless Graphical Questions MCQ
A particle which is constrained to move along the $x$ -axis, is subjected to a force in the same direction which varies with the distance $x$ of the particle from the origin as $F(x) = -kx + ax^3$ . Here $k$ and $a$ are positive constants. For $x \geq 0$ , the functional from of the potential energy $U(x)$ of the particle is
A.
B.
C.
D.
MP PMT 2001; CBSE PMT 2004 Q259 Errorless Work Done by Variable Force MCQ
A body of mass 0.1 kg moving with a velocity of 10 m/s hits a spring (fixed at the other end) of force constant 1000 N/m and comes to rest after compressing the spring. The compression of the spring is
A.
0.01m
B.
0.1m
C.
0.2m
D.
0.5m
BCECE 2001; CBSE PMT 2007; AIIMS 2008; ! Q260 Errorless Conservation of Energy and Momentum MCQ
A vertical spring with force constant $K$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$ . The net work done in the process is (images/be8937a3a0433e0f15a44a7540122b8cc89d7a194dca520d0cde82c3001f4c94.jpg)
A.
$mg(h+d)+\frac{1}{2}Kd^{2}$
B.
$mg(h+d)-\frac{1}{2}Kd^{2}$
C.
$mg(h-d)-\frac{1}{2}Kd^{2}$
D.
$mg(h-d)+\frac{1}{2}Kd^{2}$
Kerala (Engg.) 2001; EAMCET 2001; DPMT 2004; UP CPMT 2006 Q261 Errorless POWER MCQ
A truck of mass 30,000kg moves up an inclined plane of slope 1 in 100 at a speed of 30 kmph. The power of the truck is (Given $g = 10ms^{-2}$ )
A.
25 kW
B.
10 kW
C.
5 kW
D.
2.5 kW
DCE 2001, 02; Odisha JEE 2002 Q262 Errorless Elastic and Inelastic Collision MCQ
A body of mass $M_{1}$ collides elastically with another mass $M_{2}$ at rest. There is maximum transfer of energy when
A.
$M_{1} > M_{2}$
B.
$M_{1} < M_{2}$
C.
$M_{1} = M_{2}$
D.
Same for all values of $M_{1}$ and $M_{2}$
UPSEAT 2001; EAMCET 2009 Q263 Errorless Elastic and Inelastic Collision MCQ
A body at rest breaks up into 3 parts. If 2 parts having equal masses fly off perpendicularly each after with a velocity of $12m/s$ , then the velocity of the third part which has 3 times mass of each part is
A.
$4\sqrt{2} m/s$ at an angle of $45^{\circ}$ from each body
B.
$24\sqrt{2} m/s$ at an angle of $135^{\circ}$ from each body
C.
$6\sqrt{2} m/s$ at $135^{\circ}$ from each body
D.
$4\sqrt{2} m/s$ at $135^{\circ}$ from each body
2000 Q264 Allen PYQ MCQ
An electric lift with a maximum load of 2000 kg (lift + passengers) is moving up with a constant speed of $1.5 \, ms^{-1}$ . The frictional force opposing the motion is 3000 N. The minimum power delivered by the motor to the lift in watts is: $(g = 10 \, \text{ms}^{-2})$
A.
20000
B.
34500
C.
23500
D.
23000
UPSEAT 2000; CPMT 2002; Pb. PET 2004; MP PMT 2012 Q265 Errorless Work Done by Variable Force MCQ
The potential energy of a certain spring when stretched through a distance ā€˜Sā€™ is 10 joule. The amount of work (in joule) that must be done on this spring to stretch it through an additional distance ā€˜Sā€™ will be
A.
30
B.
40
C.
10
D.
20
MHCET 2000; Kerala PMT 2008; AMU PMT 2009; AIPMT (Cancelled) 2015 Q266 Errorless Work Done by Variable Force MCQ
Two similar springs P and Q have spring constants $K_{P}$ and $K_{Q}$ , such that $K_{P} > K_{Q}$ . They are stretched, first by the same amount (case a), then by the same force (case b). The work done by the springs $W_{P}$ and $W_{Q}$ are related as, in case (a) and case (b), respectively
A.
$W_{P} = W_{Q}; W_{P} = W_{Q}$
B.
$W_{P} > W_{Q}; W_{Q} > W_{P}$
C.
$W_{P} < W_{Q}; W_{Q} < W_{P}$
D.
$W_{P} = W_{Q}; W_{P} > W_{Q}$
DPMT 2000; Odisha JEE 2005 Q267 Errorless Elastic and Inelastic Collision MCQ
A mass of 100g strikes the wall with speed 5m/s at an angle as shown in figure and it rebounds with the same speed. If the contact time is $2 \times 10^{-3}$ sec, what is the force applied on the mass by the wall
A.
$250\sqrt{3}$ N to right
B.
250 N to right
C.
$250\sqrt{3}$ N to left
D.
250 N to left
2000 Q268 Objective Taking it together MCQ
A bicyclist comes to a skidding stop in 10 m. During this process, the force on the bicycle due to the road is 200 N and is directly opposed to the motion. The work done by the cycle on the road is [NCERT Exemplar]
A.
+ 2000 J
B.
- 200 J
C.
zero
D.
- 20000 J
AFMC 1999; Pb. PMT 2003 Q269 Errorless Work Done by Constant Force MCQ
The work done in pulling up a block of wood weighing 2 kN for a length of 10m on a smooth plane inclined at an angle of $15^{\circ}$ with the horizontal is $[\sin15^{\circ}=0.2588]$
A.
4.36 kJ
B.
5.17 kJ
C.
8.91 kJ
D.
9.82 kJ
RPMT 1999; DCE 2003 Q270 Errorless Elastic and Inelastic Collision MCQ
A space craft of mass 'M' and moving with velocity 'v' suddenly breaks in two pieces of same mass m. After the explosion one of the mass 'm' becomes stationary. What is the velocity of the other part of craft
A.
$\frac{Mv}{M-m}$
B.
v
C.
$\frac{Mv}{m}$
D.
$\frac{M-m}{m}v$
IIT-JEE 1999; UPSEAT 2003 Q271 Errorless Critical Thinking MCQ
A particle free to move along the x-axis has potential energy given by $U(x)=k\left[1-\exp\left(-x\right)^{2}\right]$ for $-\infty\leq x\leq+\infty$ , where k is a positive constant of appropriate dimensions. Then
A.
At point away from the origin, the particle is in unstable equilibrium
B.
For any finite non-zero value of $x$ , there is a force directed away from the origin
C.
If its total mechanical energy is $k/2$ , it has its minimum kinetic energy at the origin
D.
For small displacements from x=0, the motion is simple harmonic
RPET 1999, 2001; UPSEAT 2002 Q272 Errorless Critical Thinking MCQ
A shell is fired from a cannon with velocity v m/sec at an angle $\theta$ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon and the speed in m/sec of the other piece immediately after the explosion is
A.
$3v \cos \theta$
B.
$2v \cos \theta$
C.
$\frac{3}{2}v \cos \theta$
D.
$\frac{\sqrt{3}}{2}v \cos \theta$
CBSE PMT 1998; Kerala PET 2012 Q273 Errorless Work Done by Constant Force MCQ
A force acts on a 30 g particle in such a way that the position of the particle as a function of time is given by $x = 3t - 4t^{2} + t^{3}$ , where x is in metres and t is in seconds. The work done during the first 4 seconds is
A.
5.28 J
B.
450 mJ
C.
490 mJ
D.
530 mJ
MP PMT/PET 1998; Pb. PMT 2002 Q274 Errorless Work Done by Variable Force MCQ
Two springs of spring constants 1500 N/m and 3000 N/m respectively are stretched with the same force. They will have potential energy in the ratio
A.
4:1
B.
1:4
C.
2:1
D.
1:2
BHU 1998; EAMCET 2001; CBSE PMT 2006; WB-JEE 2008 Q275 Errorless Work Done by Variable Force MCQ
A body of mass 3 kg is under a force, which causes a displacement in it given by $S = \frac{t^{3}}{3}$ (in m). Find the work done by the force in first 2 seconds
A.
2 J
B.
3.8 J
C.
5.2 J
D.
24 J