1. A uniform spring of force constant k is cut into
two pieces, the lengths of which are in the ratio 1
: 2. The ratio of the force constants of the shorter
and the longer pieces is
a) 1 : 3
b) 1 : 2
c) 2 : 3
d) 2 : 1
Explanation:
2. A mass m =100 gms is attached at the end of a
light spring which oscillates on a frictionless
horizontal table with an amplitude equal to 0.16
metre and time period equal to 2 sec. Initially the
mass is released from rest at t = 0 and
displacement \[x=-0.16\] metre. The expression for
the displacement of the mass at any time t is
a) \[x=0.16\cos\left(\pi t\right)\]
b) \[x=-0.16\cos\left(\pi t\right)\]
c) \[x=0.16\sin\left(\pi t+\pi\right)\]
d) \[x=-0.16\sin\left(\pi t+\pi\right)\]
Explanation: Standard equation for given condition
3.A block of mass m, attached to a spring of spring
constant k, oscillates on a smooth horizontal
table. The other end of the spring is fixed to a
wall. The block has a speed v when the spring is
at its natural length. Before coming to an
instantaneous rest, if the block moves a distance x
from the mean position, then
a) \[x=\sqrt{m/k}\]
b) \[x=\frac{1}{v}\sqrt{m/k}\]
c) \[x=v\sqrt{m/k}\]
d) \[x=\sqrt{mv/k}\]
Explanation:
4. The force constants of two springs are \[k_{1}\] and
\[k_{2}\] . Both are stretched till their elastic energies
are equal. If the stretching forces are \[F_{1}\] and \[F_{2}\] ,
then \[F_{1}: F_{2}\] is
a) \[k_{1}: k_{2}\]
b) \[k_{2}: k_{1}\]
c) \[\sqrt{k_{1}}:\sqrt{ k_{2}}\]
d) \[k_1^2 :k_2^2 \]
Explanation:
5. A mass m is vertically suspended from a spring of
negligible mass; the system oscillates with a
frequency n. What will be the frequency of the system if a mass 4 m is suspended from the same
spring
a) n/4
b) 4n
c) n/2
d) 2n
Explanation:
6. If the period of oscillation of mass m suspended
from a spring is 2 sec, then the period of mass 4m
will be
a) 1 sec
b) 2 sec
c) 3 sec
d) 4 sec
Explanation:
7. Five identical springs are used in the following
three configurations. The time periods of vertical
oscillations in configurations (i), (ii) and (iii) are
in the ratio
a) \[1: \sqrt{2}:\frac{1}{\sqrt{2}}\]
b) \[2: \sqrt{2}:\frac{1}{\sqrt{2}}\]
c) \[\frac{1}{\sqrt{2}}:2:1\]
d) \[2: \frac{1}{\sqrt{2}}:1\]
Explanation:
8. If a watch with a wound spring is taken on to the
moon, it
a) Runs faster
b) Runs slower
c) Does not work
d) Shows no change
Explanation: The time period of oscillation of a spring does not depend on gravity.
9. What will be the force constant of the spring
system shown in the figure
a) \[\frac{k_{1}}{2}+k_{2}\]
b) \[\left[\frac{1}{2k_{1}}+\frac{1}{k_{2}}\right]^{-1}\]
c) \[\frac{1}{2k_{1}}+\frac{1}{k_{2}}\]
d) \[\left[\frac{2}{k_{1}}+\frac{1}{k_{2}}\right]^{-1}\]
Explanation:
10.Two springs have spring constants KA and KB
and \[k_{A}>k_{B}\] . The work required to stretch them
by same extension will be
a) More in spring A
b) More in spring B
c) Equal in both
d) Noting can be said
Explanation:
