Work, Power & Energy
769 Questions
Start Allen Test
MP PMT 1997; CBSE PMT 1998; AIIMS 2000; UPSEAT 2001; MP PET 2001, 02, 07; Kerala PMT 2008
Q326
Errorless
Elastic and Inelastic Collision
MCQ
Two equal masses $m_{1}$ and $m_{2}$ moving along the same straight line with velocities + 3 m/s and - 5 m/s respectively collide elastically. Their velocities after the collision will be respectively
A.
+4m/s for both
B.
-3 m/s and +5 m/s
C.
-4 m/s and +4 m/s
D.
$-5m / s$ and $+3m / s$
CPMT 1997; MP PET 1999; DPMT 1999, 2005; JIPMER 2000
Q327
Errorless
Perfectly Inelastic Collision
MCQ
A particle of mass m moving eastward with a speed v collides with another particle of the same mass moving northward with the same speed v. The two particles coalesce on collision. The new particle of mass 2m will move in the north-easterly direction with a velocity
A.
v/2
B.
2v
C.
$\dfrac{v}{\sqrt{2}}$
D.
v
BHU 1997; J & K CET 2010; CBSE PMT (Pre.) 2011
Q328
Errorless
Graphical Questions
MCQ
Force F on a particle moving in a straight line varies with distance d as shown in the figure. The work done on the particle during its displacement of 12 m
A.
13 J
B.
18 J
C.
21 J
D.
26 J
AFMC 1996, 2006; BHU 2001; DCE 2004, 09; AIIMS 2006; UP CPMT 2006
Q329
Errorless
Perfectly Inelastic Collision
MCQ
In an inelastic collision, what is conserved
A.
Kinetic energy
B.
Momentum
C.
Both a) and b)
D.
Neither a) nor b)
CBSE PMT 1996; MP PMT/PET 1998; AIIMS 1999; JIPMER 2001, 02; RPMT 2005
Q330
Errorless
Perfectly Inelastic Collision
MCQ
A particle of mass m moving with velocity v strikes a stationary particle of mass 2m and sticks to it. The speed of the system will be
A.
v/2
B.
2v
C.
v/3
D.
3v
Manipal MEE 1995; AIEEE 2002, 06; Pb. PET 2004; CBSE PMT 2005; KCET 2007; Odisha JEE 2008
Q331
Errorless
Conservation of Energy and Momentum
MCQ
A bomb of mass 9kg explodes into 2 pieces of mass 3kg and 6kg. The velocity of mass 3kg is 1.6 m/s, the K.E. of mass 6kg is
A.
3.84 J
B.
9.6 J
C.
1.92 J
D.
2.92 J
EAMCET (Engg.) 1995; WB-JEE 2009
Q332
Errorless
Conservation of Energy and Momentum
MCQ
Two bodies of masses 2m and m have their K.E. in the ratio 8:1, then their ratio of momenta is
A.
1:1
B.
2:1
C.
4:1
D.
8:1
CBSE PMT 1995; AIEEE 2003
Q333
Errorless
Elastic and Inelastic Collision
MCQ
A ${}^{238}U$ nucleus decays by emitting an alpha particle of speed $v\ ms^{-1}$ . The recoil speed of the residual nucleus is (in $ms^{-1}$ )
A.
-4v / 234
B.
v / 4
C.
-4v / 238
D.
4v / 238
BHU 1995; MP PET 1996; AMU (Med.) 1999; JIPMER 2000
Q334
Errorless
Critical Thinking
MCQ
A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time $t$ is proportional to
A.
$t^{1/2}$
B.
$t^{3/4}$
C.
$t^{3/2}$
D.
$t^2$
IIT-JEE 1994
Q335
Advance
ARCHIVE: JEE ADVANCED
MCQ
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 $a_{c}=k^{2}rt^{2}$ , where k is a constant. The power delivered to the particle by the force acting on it is
A.
$2\pi mk^{2}r^{2}$
B.
$mk^{2}r^{2}t$
C.
$\frac{(mk^{4}r^{2}t^{5})}{3}$
D.
Zero
IIT-JEE 1987
Q336
Advance
ARCHIVE: JEE ADVANCED
MSQ
A particle is acted upon by a force of constant magnitude which is always directed perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. From the information given, conclude that the particle
A.
has constant velocity.
B.
has constant acceleration.
C.
has constant kinetic energy.
D.
moves in a circular path.
IIT-JEE 1985
Q337
Advance
ARCHIVE: JEE ADVANCED
MCQ
A uniform chain of length L and mass M is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. The work required to pull the hanging part on the table is
A.
MgL
B.
$\frac{MgL}{3}$
C.
$\frac{MgL}{9}$
D.
$\frac{MgL}{18}$
IIT-JEE 1984
Q338
Advance
ARCHIVE: JEE ADVANCED
MCQ
A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to
A.
$t^{\frac{1}{2}}$
B.
$t^{\frac{3}{4}}$
C.
$t^{\frac{3}{2}}$
D.
$t^{2}$
IIT-JEE 1980
Q339
Advance
ARCHIVE: JEE ADVANCED
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
IIT-JEE 1980
Q340
Advance
ARCHIVE: JEE ADVANCED
MCQ
If a machine is lubricated with oil,
A.
the mechanical advantage of the machine increases
B.
the mechanical efficiency of the machine increases
C.
both its mechanical advantage and efficiency increases
D.
its efficiency increases, but its mechanical advantage decreases
1960
Q341
Advance
SINGLE CORRECT CHOICE TYPE QUESTIONS
MCQ
A 2 kg block is dropped from a height of 0.4 m on a spring of force constant $k = 1960 \, Nm^{-1}$ . The maximum compression of the spring is
A.
0.1 m
B.
0.2 m
C.
0.3 m
D.
0.4 m
1960
Q342
Advance
INTEGER/NUMERICAL ANSWER TYPE QUESTIONS
Numerical
Two blocks A and B are connected to each other by a string and a spring. The string passes over a frictionless pulley as shown in figure.
Block B slides over the horizontal top surface of a stationary block C and the block A slides along the vertical side of C, both with the same uniform speed. The coefficient of friction between the surfaces of the blocks is 0.2. The force constant of the spring is $1960 \, Nm^{-1}$ . If the mass of block A is 2 kg, calculate the mass of block B, in kg, and the energy stored in the spring in mJ. Take $g = 9.8 \, ms^{-2}$ .
Block B slides over the horizontal top surface of a stationary block C and the block A slides along the vertical side of C, both with the same uniform speed. The coefficient of friction between the surfaces of the blocks is 0.2. The force constant of the spring is $1960 \, Nm^{-1}$ . If the mass of block A is 2 kg, calculate the mass of block B, in kg, and the energy stored in the spring in mJ. Take $g = 9.8 \, ms^{-2}$ .
Correct Answer: 0.098
Explanation:
Let $m$ be the mass of $B$ . From its free-body diagram
$T - \mu N = m (0) = 0$
where $T$ is the tension in the string and $N = mg$
$\Rightarrow T = \mu (m g)$
From the free-body diagram of the spring
$T - T ^ {\prime} = 0$
where $T'$ is the force exerted by A on the spring
$\Rightarrow T = T ^ {\prime} = \mu m g$
From the free-body diagram of A
$2 g - \left(T ^ {\prime} + \mu N ^ {\prime}\right) = 2 (0) = 0$
where $N'$ is the normal reaction of the vertical wall of C on A and $N' = 2(0) = 0$ (because there is no horizontal acceleration of A)
$\Rightarrow 2 g = T ^ {\prime} = \mu m g$
$\Rightarrow m = \frac {2 g}{\mu g} = \frac {2}{0 . 2} = 1 0 \mathrm{kg}$
Tensile force on the spring is given by
$T = T ^ {\prime} = \mu m g = 0. 2 \times 1 0 \times 9. 8 = 1 9. 6 \mathrm{N}$
Now, for a spring, we have $F = kx$
$\Rightarrow 1 9. 6 = 1 9 6 0 x$
$\Rightarrow x = \frac {1}{1 0 0} \mathrm{m}$
$\Rightarrow$ Energy stored in the spring is given by
$U = \frac {1}{2} k x ^ {2} = \frac {1}{2} \times 1 9 6 0 \times \left(\frac {1}{1 0 0}\right) ^ {2} = 0. 0 9 8 \mathrm{J}$
$T - \mu N = m (0) = 0$
where $T$ is the tension in the string and $N = mg$
$\Rightarrow T = \mu (m g)$
From the free-body diagram of the spring
$T - T ^ {\prime} = 0$
where $T'$ is the force exerted by A on the spring
$\Rightarrow T = T ^ {\prime} = \mu m g$
From the free-body diagram of A
$2 g - \left(T ^ {\prime} + \mu N ^ {\prime}\right) = 2 (0) = 0$
where $N'$ is the normal reaction of the vertical wall of C on A and $N' = 2(0) = 0$ (because there is no horizontal acceleration of A)
$\Rightarrow 2 g = T ^ {\prime} = \mu m g$
$\Rightarrow m = \frac {2 g}{\mu g} = \frac {2}{0 . 2} = 1 0 \mathrm{kg}$
Tensile force on the spring is given by
$T = T ^ {\prime} = \mu m g = 0. 2 \times 1 0 \times 9. 8 = 1 9. 6 \mathrm{N}$
Now, for a spring, we have $F = kx$
$\Rightarrow 1 9. 6 = 1 9 6 0 x$
$\Rightarrow x = \frac {1}{1 0 0} \mathrm{m}$
$\Rightarrow$ Energy stored in the spring is given by
$U = \frac {1}{2} k x ^ {2} = \frac {1}{2} \times 1 9 6 0 \times \left(\frac {1}{1 0 0}\right) ^ {2} = 0. 0 9 8 \mathrm{J}$
Q343
Allen
Kinematics of Circular Motion
MCQ
Two moving particles P and Q are 10m apart at a certain instant. The velocity of P is 8m/s making an angle of $30^{\circ}$ with the line joining P and Q and Q is moving with 6m/s making an angle of $30^{\circ}$ with PQ as shown in figure. Then angular velocity of P with respect to Q is
A.
Zero
B.
0.1 rad/s
C.
0.4 rad/s
D.
0.7 rad/s
Q344
Allen
Kinematics of Circular Motion
MCQ
The second's hand of a watch has length 6 cm. Speed of end point and magnitude of difference of velocities at two perpendicular positions will be
A.
$2\pi$ and 0 mm/s
B.
$2\sqrt{2}\pi$ and 4.44 mm/s
C.
$2\sqrt{2}\pi$ and $2\pi$ mm/s
D.
$2\pi$ and $2\sqrt{2}\pi$ mm/s
Q345
Allen
Kinematics of Circular Motion
MCQ
The magnitude of displacement of a particle moving in a circle of radius $a$ with constant angular speed $\omega$ varies with time $t$ as:
A.
$2a\sin \omega t$
B.
$2a\sin \frac{\omega t}{2}$
C.
$2a\cos \omega t$
D.
$2a\cos \frac{\omega t}{2}$
Q346
Allen
Kinematics of Circular Motion
MCQ
Two particles describe the same circle of radius R in the same direction with the same speed V. then at the given instant relative angular velocity of 2 with respect to 1 will be :
A.
$\frac{2v\sin\frac{\theta}{2}}{R}$
B.
$\frac{v}{2R\sin\frac{\theta}{2}}$
C.
$\frac{v}{R}$
D.
$\frac{v\cos\frac{\theta}{2}}{R}$
Q347
Allen
Kinematics of Circular Motion
MCQ
An insect trapped in a circular groove of some radius moves along the groove steadily and completes 10 revolutions in 100s. Choose the correct statement:-
A.
The angular velocity of the insect is $10 \, \text{rad/s}$
B.
The angular velocity of the insect is $\frac{\pi}{5} \, \text{rad/s}$
C.
The angular velocity of the insect is $\frac{2\pi}{5} \, \text{rad/s}$
D.
The angular velocity of the insect can't be defined as radius is unknown.
Q348
Allen
Kinematics of Circular Motion
MCQ
At $t = 0$ a flywheel is rotating with angular velocity $\omega_0$ . It then undergoes uniform angular acceleration for a time $t_1$ , at the end of which the angular velocity is $\omega_1$ . How many revolutions did the flywheel make during this time interval?
A.
$\frac{1}{2} (\omega_0 + \omega_1)t_1$
B.
$\frac{\omega_0t_1}{2\pi}$
C.
$\frac{\omega_1t_1}{2\pi}$
D.
$\frac{(\omega_0 + \omega_1)t_1}{4\pi}$
Q349
Allen
Kinematics of Circular Motion
MCQ
Which vector in the figures best represents the acceleration of a pendulum mass at the intermediate point in its swing?
A.
B.
C.
D.
Q350
Allen
Kinematics of Circular Motion
MCQ
A particle $A$ moves along a circle of radius $R = 50 \, \text{cm}$ so that its radius vector $r$ relative to the point $O$ (figure) rotates with the constant angular velocity $\omega = 0.40 \, \text{rad/s}$ . Then modulus of the velocity of the particle, and the modulus of its total acceleration will be
A.
v = 0.4 m/s, $a = 0.4 \, m/s^{2}$
B.
$v = 0.32 \, m/s, a = 0.32 \, m/s^2$
C.
v = 0.32 m/s, $a = 0.4 \, m/s^{2}$
D.
$v = 0.4m / s, a = 0.32m / s^2$