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Work Power and Energy

505 Questions Start Allen Test
All Exams Allen Objective Errorless
Q426 Objective Taking it together MCQ
A rod of mass m and length l is lying on a horizontal table. Work done in making it stand on one end will be
A.
mgl
B.
$\frac{mgl}{2}$
C.
$\frac{mgl}{4}$
D.
2mgl
Q427 Objective Taking it together MCQ
The pointer reading versus load graph for a spring balance is as shown in the figure. The spring constant is
A.
15 kgf/cm
B.
5 kgf/cm
C.
0.1 kgf/cm
D.
10 kgf/cm
Q428 Objective Taking it together MCQ
A body of mass m was slowly pulled up the hill by a force F which at each point was directed along the tangent of the trajectory. All surfaces are smooth. Find the work performed by this force.
A.
mgl
B.
- mgl
C.
mgh
D.
zero
Q429 Objective Taking it together MCQ
Two masses of 1 g and 4 g are moving with equal kinetic energies. The ratio of the magnitudes of their momenta is
A.
4:1
B.
$\sqrt{2}$ :1
C.
1:2
D.
1:16
Q430 Objective Taking it together MCQ
If v, p and E denote velocity, linear momentum and kinetic energy of the particle respectively, then
A.
$p = \frac{dE}{dv}$
B.
$p = \frac{dE}{dt}$
C.
$p = \frac{dv}{dt}$
D.
$p = \frac{dE}{dv} \times \frac{dE}{dt}$
Q431 Objective Taking it together MCQ
The energy required to accelerate a car from rest to $10 \, ms^{-1}$ is W. The energy required to accelerate the car from $10 \, ms^{-1}$ to $20 \, ms^{-1}$ is
A.
W
B.
2 W
C.
3 W
D.
4 W
Q432 Objective Taking it together MCQ
Which of the following diagrams most closely shows the variation in kinetic energy of the earth as it moves once around the sun in its elliptical orbit? [NCERT Exemplar]
A.
B.
C.
D.
Q433 Objective Taking it together MCQ
A particle is moved from $(0,0)$ to $(a,a)$ under a force $\mathbf{F} = (3\hat{\mathbf{i}} + 4\hat{\mathbf{j}})$ from two paths. Path 1 is OP and path 2 is OQP. Let $W_{1}$ and $W_{2}$ be the work done by this force in these two paths. Then,
A.
$W_{1} = W_{2}$
B.
$W_{1} = 2W_{2}$
C.
$W_{2} = 2W_{1}$
D.
$W_{2} = 4W_{1}$
Q434 Objective Taking it together MCQ
A body moves from rest with a constant acceleration. Which one of the following graphs represents the variation of its kinetic energy K with the distance travelled x?
A.
B.
C.
D.
Q435 Objective Taking it together MCQ
Which of the following diagrams represents variation of total mechanical energy of a pendulum oscillating in air as function of time? [NCERT Exemplar]
A.
B.
C.
D.
Q436 Objective Taking it together MCQ
An object of mass m, initially at rest under the action of a constant force F attains a velocity v in time t. Then, the average power supplied to mass is
A.
$\frac{mv^{2}}{2t}$
B.
$\frac{Fv}{2}$
C.
Both a) and b)
D.
None of these
Q437 Objective Taking it together MCQ
A particle at rest on a frictionless table is acted upon by a horizontal force which is constant in magnitude and direction. A graph is plotted for the work done on the particle W against the speed of the particle v. If there are no frictional forces acting on the particle, the graph will look like
A.
B.
C.
D.
Q438 Objective Taking it together MCQ
A car moving with a speed of $40 \, kmh^{-1}$ can be stopped by applying brakes in 2 m. If the car is moving with a speed of $80 \, kmh^{-1}$ , the minimum stopping distance under similar brakes will be
A.
8 m
B.
2 m
C.
4 m
D.
6 m
Q439 Objective Taking it together MCQ
A long spring is stretched by 2 cm. Its potential energy is U. If the spring is stretched by 10 cm, its potential energy would be
A.
$\frac{U}{25}$
B.
$\frac{U}{5}$
C.
5U
D.
25U
Q440 Objective Taking it together MCQ
A body is falling under gravity. When it loses a gravitational potential energy by U, its speed is v. The mass of the body will be
A.
$\frac{2U}{v}$
B.
$\frac{U}{2v}$
C.
$\frac{2U}{v^{2}}$
D.
$\frac{U}{2v^{2}}$
Q441 Objective Taking it together MCQ
How much mass is converted into energy per day in Tarapur nuclear power plant operated at $10^{7}$ kW?
A.
9.6 g
B.
9.63 kg
C.
8.6 g
D.
7 g
Q442 Objective Taking it together MCQ
A proton is kept at rest. A positively charged particle is released from rest at a distance d in its field. Consider two experiments: one in which the charged particle is also a proton and in another a positron. In the same time t, the work done on the two moving charged particles is [NCERT Exemplar]
A.
same as the same force law is involved in the two experiments
B.
less for the case of a positron, as the positron moves away more rapidly and the force on it weakens
C.
more for the case of a positron, as the positron moves away a larger distance
D.
same as the work done by charged particle on the stationary proton
Q443 Objective Taking it together MCQ
The potential energy function for a particle executing linear SHM is given by $V(x) = \frac{1}{2} kx^{2}$ where, k is the force constant of the oscillator (see figure). For $k = 0.5 Nm^{-1}$ , the graph of $V(x)$ versus x is shown in the figure. A particle of total energy E turns back when it reaches $x = \pm x_{m}$ . If V and K indicate the PE and KE respectively of the particle at $x = +x_{m}$ , then which of the following is correct? [NCERT Exemplar]
A.
V = 0, K = E
B.
V = E, K = 0
C.
V < E, K = 0
D.
V = 0, K < E
Q444 Objective Taking it together MCQ
The potential energy between the atoms in a molecule is given by $U(x)=\frac{a}{x^{12}}-\frac{b}{x^{6}}$ where, a and b are positive constants and x is the distance between the atoms. The atom is in equilibrium when
A.
x = 0
B.
$x = \left(\frac{a}{2b}\right)^{1/6}$
C.
$x = \left(\frac{2a}{b}\right)^{1/6}$
D.
$x = \left(\frac{11a}{5b}\right)^{1/6}$
Q445 Objective Taking it together MCQ
A ball is thrown vertically upwards with a velocity of $10 \, ms^{-1}$ . It returns to the ground with a velocity of $9 \, ms^{-1}$ . If $g = 9.8 \, ms^{-2}$ , then the maximum height attained by the ball is nearly (assume air resistance to be uniform)
A.
5.1 m
B.
4.1 m
C.
4.61 m
D.
5 m
Q446 Objective Taking it together MCQ
A body is moving down an inclined plane of slope $37^{\circ}$ . The coefficient of friction between the body and plane varies as $\mu = 0.3x$ , where x is the distance travelled down the plane by the body. The body will have maximum speed (Take, $g = 10 \, ms^{-2}$ , $\sin 37^{\circ} = \frac{3}{5}$ )
A.
at x = 1.16 m
B.
at x = 2 m
C.
at bottom of plane
D.
at x = 2.5 m
Q447 Objective Taking it together MCQ
A mass-spring system oscillates such that the mass moves on a rough surface having coefficient of friction $\mu$ . It is compressed by a distance a from its normal length and on being released, it moves to a distance b from its equilibrium position. The decrease in amplitude for one half-cycle (-a to b) is
A.
$\frac{\mu mg}{k}$
B.
$\frac{2\mu mg}{k}$
C.
$\frac{\mu g}{k}$
D.
$\frac{k}{\mu mg}$
Q448 Objective Taking it together MCQ
A block of mass 5 kg slides down a rough inclined surface. The angle of inclination is $45^{\circ}$ . The coefficient of sliding friction is 0.20. When the block slides 10 cm, the work done on the block by force of friction is
A.
$-\frac{1}{\sqrt{2}}J$
B.
1J
C.
$-\sqrt{2}J$
D.
-1J
Q449 Objective Taking it together MCQ
The system shown in the figure is released from rest. At the instant when mass M has fallen through a distance h, the velocity of m will be
A.
$\sqrt{2gh}$
B.
$\frac{\sqrt{2ghM}}{m}$
C.
$\sqrt{\frac{2gh(M - m)}{m + M}}$
D.
$\sqrt{\frac{2gh(M + m)}{m - M}}$
Q450 Objective Taking it together MCQ
The curved portions are smooth and horizontal surface is rough. The block is released from P. At what distance from A, it will stop (if $\mu = 0.2$ )?
A.
$1\mathrm{m}$
B.
$2\mathrm{m}$
C.
$3\mathrm{m}$
D.
$4\mathrm{m}$