Work, Power & Energy
238 Questions
Start Errorless Test
BHU 1997; MP PET 2000; CBSE PMT 2000; MH CET 2000; JIPMER 2001, 02; AMU (Med.) 2002; DPMT 2003
Q226
Errorless
4. Power
MCQ
The power of a pump, which can pump 200kg of water to a height of 200m in 10sec is $(g=10m/s^{2})$
A.
40 kW
B.
80 kW
C.
400 kW
D.
960 kW
MP PMT 1997; CBSE PMT 1998; AIIMS 2000; UPSEAT 2001; MP PET 2001, 02, 07; Kerala PMT 2008
Q227
Errorless
5. 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
Q228
Errorless
6. 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
Q229
Errorless
8. 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
Q230
Errorless
6. 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
Q231
Errorless
6. 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
Q232
Errorless
3. 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
Q233
Errorless
3. 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
Q234
Errorless
5. 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
Q235
Errorless
7. 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.
$t^2$
Q236
Errorless
7. Critical Thinking
MCQ
A body of mass $(5 \pm 0.5)$ kg is moving with a velocity of $(20 \pm 0.4)$ m/s. Its kinetic energy will be
A.
$(1000 \pm 140)J$
B.
$(1000 \pm 0.14)J$
C.
$(500 \pm 0.14)J$
D.
$(500 \pm 140)J$
Q237
Errorless
8. Graphical Questions
MCQ
A force $F$ acting on an object varies with distance $x$ as shown here. The force is in newton and $x$ in metre. The work done by the force in moving the object from $x = 0$ to $x = 6 m$
A.
$4.5 J$
B.
$13.5 J$
C.
$9.0 J$
D.
$18.0 J$
Q238
Errorless
9. JEE Section
Numerical
A ball is thrown from the location $(x_{0},y_{0})=(0,0)$ of a horizontal playground with an initial speed $v_{0}$ at an angle $\theta_{0}$ from the +x-direction. The ball is to be hit by a stone, which is thrown at the same time from the location $(x_{1},y_{1})=(L,0)$ . The stone is thrown at an angle $(180-\theta_{1})$ from the +x-direction with a suitable initial speed. For a fixed $v_{0}$ , when $(\theta_{0},\theta_{1})=(45^{\circ},45^{\circ})$ , the stone hits the ball after time $T_{1}$ , and when $(\theta_{0},\theta_{1})=(60^{\circ},30^{\circ})$ , it hits the ball after time $T_{2}$ . In such a case, $(T_{1}/T_{2})^{2}$ is ____
Correct Answer: 2
Explanation:
For case I :
$a_{rel} = 0$
For collision $\frac{v_0}{\sqrt{2}} = \frac{v}{\sqrt{2}}$
$\therefore v = v_{0}$
So, $T_{1} = \frac{L}{\frac{v_{0}}{\sqrt{2}} + \frac{v}{\sqrt{2}}}$
$\therefore T_{1} = \frac{L}{\sqrt{2}v_{0}}$
... (i)
For case II :
$a_{rel} = 0$
For collision, $\frac{v_0\sqrt{3}}{2} = \frac{v}{2}$
$\therefore v = \sqrt{3} v_{0}$
So, $T_{2} = \frac{L}{\frac{v_{0}}{2} + v\frac{\sqrt{3}}{2}} \Rightarrow T_{2} = \frac{L}{\frac{v_{0}}{2} + \frac{3v_{0}}{2}}$
$\therefore T_{2} = \frac{L}{2v_{0}}$
... (ii)
So, $\left(\frac{T_1}{T_2}\right)^2 = (\sqrt{2})^2 = 2\Rightarrow \left(\frac{T_1}{T_2}\right)^2 = 2$
$a_{rel} = 0$
For collision $\frac{v_0}{\sqrt{2}} = \frac{v}{\sqrt{2}}$
$\therefore v = v_{0}$
So, $T_{1} = \frac{L}{\frac{v_{0}}{\sqrt{2}} + \frac{v}{\sqrt{2}}}$
$\therefore T_{1} = \frac{L}{\sqrt{2}v_{0}}$
... (i)
For case II :
$a_{rel} = 0$
For collision, $\frac{v_0\sqrt{3}}{2} = \frac{v}{2}$
$\therefore v = \sqrt{3} v_{0}$
So, $T_{2} = \frac{L}{\frac{v_{0}}{2} + v\frac{\sqrt{3}}{2}} \Rightarrow T_{2} = \frac{L}{\frac{v_{0}}{2} + \frac{3v_{0}}{2}}$
$\therefore T_{2} = \frac{L}{2v_{0}}$
... (ii)
So, $\left(\frac{T_1}{T_2}\right)^2 = (\sqrt{2})^2 = 2\Rightarrow \left(\frac{T_1}{T_2}\right)^2 = 2$