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Here is a picture of a B-52 located at the Pima air and space museum.
B-52
Source:(www.airplaneexhibits.com)

As you can see in the picture on the right wing next to one of the engines there is some kind of missile carrier, but the left wing has no missile carrier. Wouldn't the weight of the aircraft be very unbalanced with a missile on the right side, but no missile on the left side. I have noticed this in a lot of pictures of B-52's where they are carrying a missile on the right wing, but no missile on the left one.

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    $\begingroup$ This particular missile was called North American X-15. It was indeed rocket-powered, but also hat a pilot onboard. See here for more. $\endgroup$ – Peter Kämpf Sep 29 '15 at 22:31
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    $\begingroup$ Is that photograph's left or plane's left? $\endgroup$ – DJohnM Sep 29 '15 at 22:34
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    $\begingroup$ @DJohnM From looking at the picture it on the left side, but its really on the right side. $\endgroup$ – Ethan Sep 29 '15 at 22:36
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@Peter is right.

The aircraft in question is the "The High and Mighty One" a NB-52A serial number 52-0003, which was used as a launch aircraft for the North American X-15, a hypersonic rocket powered aircraft. The 'missile carrier' (pylon) is used for carrying the X-15.

Here is a view of the carrier itself, just after launching.

X- 15 release
"X-15 launched bw". Licensed under Public Domain via Commons.

This was used as the X-15 was not designed to takeoff under its own power; it was rather designed to be carried aloft and drop launched from under the wing of a NASA B-52 'mother ship'. As of March 2016, the X-15 holds the official world record for the highest speed ever reached by a manned, powered aircraft.

X-15 mounting
Image from air-and-space.com; Photo courtesy North American Rockwell.

The aircraft underwent significant modifications for installation of the pylon, including removal of the wing (no. 3) fuel tank, disabling the inboard flaps in the starboard wing and cutting a notch to accommodate the X-15's vertical stabilizer.

The heaviest weight the aircraft carried on the pylon was ~53,100 lb, for X-15 with external fuel tanks. A number of tests were carried out and it was found that the carrier aircraft were capable of trimming out the unbalance of the B-52/X-15 combination. So this caused few problems in flight in the operational range.

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    $\begingroup$ I would imagine that the weight of the X-15 was nearly offset by the missing #3 fuel tank. $\endgroup$ – FreeMan Mar 8 '16 at 13:21
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    $\begingroup$ @FreeMan But then, on the launch, you get some significant side-kick :) $\endgroup$ – yo' Mar 8 '16 at 19:17
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    $\begingroup$ @yo' that's true, then when it's gone, you've got all that weight missing and no wing tank to pump fuel into to balance things back out. But, as the answer said, they were able to trim it back into balance, so it was all good. $\endgroup$ – FreeMan Mar 8 '16 at 19:18

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